Chapter 12 — Sound

What produces sound? Sound is produced when an object vibrates. The vibration of the source sets neighbouring particles of a medium (air, water or solid) into back-and-forth motion, creating regions of compression and rarefaction that travel as a longitudinal wave. Human ears detect these pressure variations as sound.

How the process works (step-by-step)

• Initial disturbance: a body (string, air column, membrane, tuning fork, speaker cone) is set into oscillatory motion.
• Local particle motion: oscillating object pushes and pulls nearby particles, producing alternate compressions (high pressure) and rarefactions (low pressure).
• Wave propagation: these pressure variations travel through the medium as longitudinal waves — the sound wave carries energy but not matter.
• Reception: when the wave reaches a detector (ear, microphone), it causes a mechanical or electrical response interpreted as sound.

Key properties determined by the source and medium

• Frequency (f) — number of vibrations per second (unit: Hz). Determines the pitch: higher f → higher pitch.
• Amplitude — maximum displacement/pressure variation. Determines loudness: larger amplitude → louder sound.
• Wave speed (v) — depends on the medium (and its temperature). In air at 20°C, v ≈ 343 m/s.
• Wavelength (λ) — distance between successive compressions. Related to v and f by v = fλ.

Important related phenomena

• Resonance: When an object is forced to vibrate at its natural frequency by an external vibrating source, amplitudes increase dramatically (e.g., a tuning fork causing another identical tuning fork to vibrate, or a swing being pushed at the right rate).
• Requirement of a medium: Sound cannot travel in vacuum. Demonstration: a ringing bell placed inside a vacuum bell jar becomes inaudible as air is removed, even though the bell still vibrates.

Practical sources and how they produce vibrations

• Tuning fork: struck prongs vibrate producing alternating pressure pulses in air — clear nearly pure tone (single frequency).
• Stringed instrument: plucked/vibrated string oscillates; frequency depends on length, tension and linear density (shorter/tenser/thinner → higher pitch).
• Wind instrument: air column inside tube vibrates; standing waves form producing notes determined by tube length and whether ends are open or closed.
• Drum: stretched membrane vibrates producing complex mixtures of frequencies (timbre).
• Loudspeaker: electrical signal causes cone to oscillate, pushing air to create sound waves.

Human hearing range and units

• Typical hearing range: about 20 Hz to 20 000 Hz (20 kHz).
• Amplitude related measure: sound intensity level measured in decibels (dB).

This covers the basic physics of how sound is produced, how it propagates and what source properties control the character (pitch, loudness, timbre) of the sound.

What is needed for sound to travel? Sound is a mechanical wave produced by vibrating objects. It requires a material medium (solid, liquid or gas) made of particles to travel. Particles of the medium oscillate about their mean positions and transfer the disturbance (energy) from one particle to the next by collisions or elastic forces. In the absence of particles (a vacuum) there is no mechanism for transfer and sound cannot propagate.

Type of sound wave and how it propagates

• Sound in gases and liquids: longitudinal waves — particles oscillate parallel to the direction of wave travel, creating compressions (regions of high pressure) and rarefactions (regions of low pressure).
• Sound in solids: can propagate as longitudinal and also as transverse (shear) waves because solids have rigidity. Generally, sound travels fastest in solids, slower in liquids, and slowest in gases.

Why a medium is necessary (physical picture)

• Vibrating source sets nearby particles into motion. These particles interact with neighbors (via collisions or elastic forces), passing on the disturbance. This chain of local interactions transports energy as a wave.
• In a vacuum there are no particles to interact, hence no transmission—sound cannot be heard.

Dependence of speed on medium and conditions

• Speed of sound depends on the medium’s elastic property (how easily it restores after compression) and its inertia (density). Greater elasticity → higher speed; greater density → lower speed (all else equal).
• For gases, temperature strongly affects speed: higher temperature → faster molecular motion → higher speed of sound.

Important consequences

• Frequency of a source remains the same when sound passes from one medium to another, but wavelength changes because v = fλ.
• Phenomena such as reflection, refraction, attenuation and diffraction occur during propagation and depend on medium properties and geometry.

Simple experimental evidence: A ringing bell placed inside an evacuated glass jar becomes inaudible as air is removed—showing sound needs a medium. If the bell is touched to the jar, vibrations travel through the solid glass and the bell can be heard outside.

What is sound? Sound is a form of energy produced by vibrating objects. It travels as a mechanical wave through a material medium (solid, liquid or gas) by successive compressions and rarefactions of the particles of the medium.

Longitudinal wave: Sound waves are longitudinal waves — the particles of the medium oscillate parallel to the direction of wave propagation. Regions where particles are close together are called compressions, and regions where they are spread out are called rarefactions.

Key characteristics:

• Medium required: Sound needs a material medium; it cannot travel through vacuum.
• Energy transfer without matter transport: Energy moves through the medium while individual particles oscillate about fixed positions.
• Amplitude: Maximum displacement of a particle from its mean position — related to the loudness (larger amplitude → louder sound).
• Wavelength (λ): Distance between two successive compressions or rarefactions.
• Frequency (f): Number of vibrations (cycles) per second — determines pitch. Unit: hertz (Hz).
• Time period (T): Time for one complete vibration, T = 1/f.
• Speed (v): How fast the wave travels in the medium; depends on the medium and temperature.

Dependence on medium and temperature: Sound travels fastest in solids, slower in liquids, and slowest in gases because particle interactions are strongest in solids. In air, speed increases with temperature. Approximate formula for speed of sound in air near 0–100°C: v ≈ 331 + 0.6T (m/s), where T is in °C.

Audible range and classifications: Humans typically hear sounds between about 20 Hz and 20,000 Hz. Frequencies below this are infrasonic, and above are ultrasonic. Ultrasonic waves are used in medical imaging and sonar.

Wave phenomena: Sound exhibits reflection (echo), refraction (change of speed in different media), diffraction (bending around obstacles), interference (superposition of waves), and absorption (energy loss in the medium).

In summary: sound is a mechanical, longitudinal wave that transfers energy via compressions and rarefactions of a medium; its perceptible properties (pitch, loudness, quality) arise from frequency, amplitude and waveform.

What is a wave? A wave is a disturbance that transfers energy and information from one place to another without the bulk transport of matter. Waves can be mechanical (require a medium, e.g. sound, water waves) or electromagnetic (do not require a medium, e.g. light).

Types by particle motion: Transverse waves — particles move perpendicular to the direction of wave propagation (e.g. waves on a string, water surface waves). Longitudinal waves — particles move parallel to the direction of propagation (e.g. sound waves: compressions and rarefactions).

Key wave parameters (with symbols and units):

• Amplitude (A): maximum displacement of a particle from its mean position. Unit: metre (m). For sound waves amplitude is related to pressure variation and loudness.
• Wavelength (λ): shortest distance between two points in phase on successive cycles (e.g., crest to crest or compression to compression). Unit: metre (m).
• Time period (T): time taken for one complete oscillation of a particle or for one complete wave cycle to pass a point. Unit: second (s).
• Frequency (f): number of complete oscillations or cycles per second. Unit: hertz (Hz). Relation: f = 1/T.
• Wave speed (v): speed at which the wave disturbance travels through the medium. Unit: metre per second (m/s).
• Phase (φ): a measure (in degrees or radians) of the stage of the cycle at a given time and place; important for interference but not always required at Class 9 level.

Relation between parameters:

In the time equal to one period T, a wave travels exactly one wavelength λ. Therefore the wave speed v is distance/time = λ/T. Using f = 1/T this gives the fundamental relation:

v = f × λ

So: f = v/λ and T = 1/f. These formulas let you find any one parameter if the other two are known.

Wave (sinusoidal) equation — compact form (optional):

y(x,t) = A sin(kx - ωt + φ), where k = 2π/λ is the wave number and ω = 2πf is the angular frequency. This form shows how displacement y depends on position x and time t.

Notes specific to sound:

• Sound is a longitudinal mechanical wave consisting of compressions (high pressure) and rarefactions (low pressure).
• Frequency determines pitch (higher f → higher pitch). Amplitude (pressure amplitude) determines loudness.
• Speed of sound in air at 20°C ≈ 343 m/s (depends on temperature and medium).

Simple derivation example: If a source emits 440 cycles per second (A4 musical note), f = 440 Hz. In air with v = 343 m/s, wavelength λ = v/f = 343/440 ≈ 0.78 m.

Pitch
Pitch is the perceptual attribute of sound that allows us to judge how high or low a note sounds. Pitch depends mainly on the frequency of vibration: higher frequency → higher pitch. Frequency (f) is measured in hertz (Hz).

Key relations: f = 1/T (T = time period), and for a wave v = f \lambda (v = wave speed, \lambda = wavelength). A pure sine tone of 440 Hz (the musical A) sounds higher in pitch than a 220 Hz tone.

Loudness
Loudness is the subjective perception of sound intensity. Objectively we use intensity (I), the sound power per unit area (W/m²), and amplitude (A) of the wave. Intensity is proportional to the square of amplitude: I \propto A^2. Human hearing measures loudness on a logarithmic decibel (dB) scale: \beta = 10 \log_{10}(I/I_0), where I_0 = 10^{-12} W/m² is a reference threshold of hearing.

Loudness is also affected by distance (for a point source, intensity falls roughly as 1/r^2) and by frequency because the ear is more sensitive to some frequencies than others.

Quality (Timbre)
Timbre (also called quality or tone colour) is what makes two sounds with the same pitch and loudness sound different. Timbre depends on the waveform shape and the relative strengths of the fundamental frequency and its harmonics (overtones). A tuning fork produces a nearly pure sine wave (few harmonics) so its timbre is smooth. A violin or flute playing the same note has different harmonic content, so each instrument has a distinct timbre.

Additional points

• Two tones with the same frequency and amplitude but different harmonic content will have different timbre.
• Pitch perception is not strictly linear with frequency; musical systems use logarithmic spacing (an octave doubles frequency).
• Physical factors controlling pitch: length, tension and mass per unit length of a vibrating string; for air columns: length and whether ends are open/closed.

What is range of hearing?
The range of hearing is the span of frequencies that the average human ear can detect. For a healthy young person this is approximately 20 Hz to 20,000 Hz (20 kHz). Sounds below 20 Hz are called infrasound and sounds above 20 kHz are called ultrasound. The exact limits vary with age and individual; the upper limit typically falls with age.

Classification by frequency

• Infrasound: < 20 Hz. Long wavelengths, produced by earthquakes, volcanic activity, large machinery, and some animal communications (e.g., elephants).
• Audible sound: 20 Hz – 20 kHz. Includes speech, music, environmental noises.
• Ultrasound: > 20 kHz. Used by bats and dolphins for echolocation, by medical imaging devices, and in industrial cleaning.

Classification by intensity (loudness)
Sound is also classified by intensity (or loudness). Intensity is the power per unit area carried by a sound wave. The faintest sound a young ear can detect has intensity about I₀ = 1×10⁻¹² W/m² (defined as 0 dB). Sounds around 120 dB (I ≈ 1 W/m²) cause pain and can damage hearing.

Important notes

• Human sensitivity is not uniform across frequency: the ear is most sensitive in the 2–5 kHz range (important for understanding speech).
• Age, prolonged exposure to loud sounds, and certain illnesses reduce hearing range (especially the high-frequency end).

How frequency relates to wavelength
For any sound wave, frequency f, wavelength λ, and wave speed v are related by v = f λ. In air at about 20 °C, v ≈ 343 m/s, so a 20 Hz sound has λ ≈ 17 m while a 20 kHz sound has λ ≈ 0.017 m (1.7 cm).

What is speed of sound?

Speed of sound is the distance travelled by a sound wave per unit time. It tells how fast a sound disturbance moves through a medium. Symbolically, speed of sound is usually denoted by v (or c) and has SI unit metres per second (m/s).

Basic relation

For a wave, speed v, frequency f and wavelength λ are related by:
v = f λ

How the medium affects speed

Sound needs a material medium (solid, liquid or gas) to travel. The speed depends mainly on two properties of the medium:

• Elasticity (ability to restore shape) — higher elasticity speeds up sound.
• Density (mass per unit volume) — greater density tends to slow sound, but the effect is combined with elasticity.

Because solids are very elastic and their particles are closely packed, sound travels fastest in solids, slower in liquids, and slowest in gases.

Temperature dependence (in gases)

In gases (like air), speed increases with temperature because particles move more and transmit vibrations faster. A commonly used approximate formula for dry air is:

v = 331 m/s + 0.6 m/s × T, where T is temperature in °C.

So at 0°C, v ≈ 331 m/s; at 20°C, v ≈ 331 + 0.6×20 = 343 m/s.

Other useful relations

For fluids (liquids and gases) a more general relation is v = sqrt(B/ρ), where B is the bulk modulus (measure of incompressibility) and ρ is density. For solids, v ≈ sqrt(E/ρ), where E is Young's modulus (measure of stiffness). These show that larger elastic modulus and lower density give higher speed.

Measuring speed using echo

An easy method is to use an echo. If a sound pulse is sent and the echo returns after time t, and the reflecting surface is at distance d, then the sound travels twice the distance (to the wall and back) in time t. Thus d = v t/2, or v = 2d / t. This is used in experiments and in sonar/ultrasound devices.

Typical speeds (approximate)

• Air (at 20°C): 343 m/s
• Water: ≈ 1480 m/s
• Steel: ≈ 5000–6000 m/s

Why this matters in daily life

Knowing the speed of sound explains why we see lightning before hearing thunder, how echolocation and sonar work, and why musical instruments produce tones with specific wavelengths. It also underlies technologies like ultrasound imaging and acoustic ranging.

What is reflection of sound?
Reflection of sound is the bouncing back of sound waves from a surface when they encounter a boundary between two media. Like light, sound obeys the laws of reflection and can produce phenomena such as echoes and reverberation.

Laws of reflection of sound

• Incident sound ray, reflected sound ray and the normal at the point of incidence all lie in the same plane.
• Angle of incidence = Angle of reflection (measured from the normal).

How echo forms
When a sound wave hits a large, smooth, hard surface, part of its energy is reflected back. If the reflected sound reaches the listener with a time delay large enough to be perceived separately from the original sound, it is heard as an echo. The human ear requires a minimum time gap of about 0.1 s to distinguish an echo from the original sound.

Condition for a distinct echo
Let v be speed of sound and d the one-way distance between source (or listener) and reflecting surface. The sound travels to the surface and back, so time t = 2d / v. For distinct echo, t >= 0.1 s, so d >= v * 0.1 / 2. For v ≈ 340 m/s this gives d >= 17 m.

Reverberation
If reflected sounds arrive in quick succession (within about 0.1 s), they blend with the original sound and produce a prolonged sound called reverberation. Reverberation is common in rooms with many reflecting surfaces; some reverberation is desirable (music halls) but excessive reverberation spoils speech clarity. Materials that absorb sound (curtains, carpets) reduce reverberation.

Key points

• Reflection works for longitudinal (sound) waves as for transverse (light) waves.
• Reflection does not change the frequency of sound; pitch remains same. Amplitude and intensity may decrease due to energy loss.
• Concave reflecting surfaces can focus sound to a point (used in whispering galleries, parabolic microphones).

Applications
Echo and reflection are used in SONAR, medical ultrasound imaging, architectural acoustics (design of auditoria), echo-location by bats and dolphins, and directional microphones/reflectors.

Reverberation is the persistence of sound in an enclosed space after the source has stopped, caused by repeated reflections of sound waves from walls, floor, ceiling and objects. Instead of a single reflected sound (an echo), reverberation is a rapid succession of many reflected sounds that overlap and produce a prolonged decay of sound.

Reverberation time (often called T or T60) is the time required for the sound intensity (or sound level) to decrease by 60 dB after the source stops. Longer reverberation time means sound lingers; shorter time means sound dies out quickly. The cause of reverberation is the finite amount of sound energy absorbed by surfaces and air—when absorption is small, reflections keep the sound alive longer.

Acoustics is the science of sound—how sound is produced, transmitted and received in a space. Architectural acoustics studies how room shape, size, surface materials and contents affect sound. Good acoustics means that speech is intelligible and music sounds balanced; this often requires controlling reverberation and reflections.

Key ideas:

• Reverberation vs Echo: An echo is a distinct reflected sound heard separately (time delay > ~0.1–0.2 s for human ears). Reverberation is many overlapping reflections that cause a decay.
• Reverberation time depends on room volume and total absorption. Bigger rooms with hard, reflective surfaces have longer reverberation times.
• Acoustic treatment (curtains, carpets, foam panels) increases absorption and reduces reverberation, improving speech clarity.

Practical significance: For classrooms and lecture halls you want relatively short reverberation times (clear speech); for concert halls longer times may be desirable for musical richness. Proper acoustic design balances clarity and warmth depending on the purpose of the space.

Introduction
Reflection of sound (echo) is used by animals and instruments to detect objects and measure distances. Two important applications are echolocation (used by bats, dolphins, etc.) and SONAR (used by ships and submarines).

Echolocation (biological sonar)
Many animals emit high‑frequency (ultrasonic) sounds and listen for the echoes reflected from obstacles or prey. By measuring the time interval between the emitted sound and the received echo, the animal estimates the distance to the object.

• Working principle: Animal emits a sound pulse → sound travels to object → part of energy reflects back → animal receives echo.
• Distance calculation: If the round‑trip time is t and the speed of sound in air is v, the distance to the object (d) is d = v × t / 2.
• Frequencies: Bats: ~20–200 kHz; dolphins: ~40–150 kHz. Higher frequencies give better resolution but shorter range.

Human perception note: Humans can hear an echo only if the reflected sound returns after about 0.1 s or more because echoes arriving sooner are perceived as part of the original sound. With v ≈ 343 m/s (at 20 °C), the minimum distance for a distinct echo is about 17 m (d = v × 0.1 / 2 ≈ 17.15 m).

Example (echolocation):
Object at 50 m from a bat, speed of sound in air v = 343 m/s
Round‑trip time t = 2d / v = 2×50 / 343 ≈ 0.292 s
The bat hears the echo after ≈ 0.292 s.

SONAR (Sound Navigation And Ranging)
SONAR is a human-made system that works on the same reflection principle. An active sonar device emits short sound pulses (pings) into water and listens for echoes from the seafloor, underwater objects or marine life.

• Types: Active SONAR (sends pulses and listens for echoes) and passive SONAR (listens for sounds made by objects).
• Distance/depth measurement: Using the round‑trip time t of the pulse, distance (or depth) d = v_water × t / 2.
• Typical sound speeds: In seawater v ≈ 1500 m/s (depends on temperature, salinity, pressure); in freshwater near 20 °C v ≈ 1480 m/s.

Example (SONAR depth measurement):
If a sonar ping returns after t = 0.4 s and v_water = 1500 m/s,
Depth d = v × t / 2 = 1500 × 0.4 / 2 = 300 m.
So the seabed is about 300 m below the sonar.

Practical uses

• Navigation and obstacle avoidance for ships and submarines.
• Depth sounding (measuring ocean depth), mapping seafloor.
• Fish finders for locating schools of fish.
• Wildlife: bats and dolphins locate prey and navigate in the dark.

Limitations & factors affecting performance

• Absorption: Higher frequencies are absorbed more quickly in water and air, reducing range.
• Temperature, salinity and pressure in water change the speed of sound and affect range/accuracy.
• Surface noise, multipath reflections and scattering reduce clarity of echoes.

Summary
Echolocation and SONAR both use reflection of sound. By measuring the time between emission and echo and using the speed of sound in the medium, we can calculate distances. Biological systems use ultrasonic frequencies for high resolution; human SONAR systems choose frequency depending on required range and resolution.

What is ultrasound?

Ultrasound is sound with frequency above the audible range for humans (greater than about 20 kHz). In practice, ultrasonic waves used in technology and medicine range from a few tens of kilohertz to several tens of megahertz.

How ultrasound is produced and detected

• Ultrasound is commonly produced by a piezoelectric crystal in a transducer. When an alternating voltage is applied, the crystal changes shape rapidly and emits ultrasonic waves. The same crystal can receive returning echoes: incoming pressure waves deform the crystal and generate electrical signals.

Key physical properties

• Short wavelength at high frequency: wavelength λ = v / f (v is wave speed, f is frequency). Shorter wavelength gives better ability to resolve small objects.
• Reflection and transmission at boundaries: when ultrasound meets a boundary between materials of different acoustic impedance, part of the wave is reflected (echo) and part transmitted. The strength of echoes depends on the impedance difference.
• Attenuation: ultrasound intensity decreases with distance due to absorption and scattering. Higher frequencies attenuate faster.

Major uses of ultrasound

• Medical imaging (ultrasonography): producing real-time images of internal body structures (e.g., fetal imaging, abdominal organs) using reflected echoes.
• Doppler ultrasound: measuring blood flow and velocities by detecting frequency shifts of the reflected waves.
• Therapeutic ultrasound: physiotherapy for deep heating of tissues and focused ultrasound for breaking kidney stones (lithotripsy).
• Cleaning: ultrasonic cleaners use high-frequency vibrations in a liquid to remove dirt from small, delicate objects like jewelry and surgical instruments.
• Nondestructive testing (NDT): detecting flaws/cracks in metals and materials by sending pulses and analysing echoes.
• SONAR and ranging: detecting objects and measuring distances under water (submarines, depth sounding) using sound pulses and echoes.
• Animal echolocation and animal devices: bats use ultrasonic echolocation; dog whistles produce ultrasound that dogs hear but humans do not.

Safety and limitations

• Diagnostic ultrasound is generally safe because it uses non-ionizing mechanical waves. However, care is taken to limit exposure to necessary durations and intensities.
• Higher frequency gives better resolution but lower penetration because of greater attenuation; choice of frequency is a trade-off between resolution and depth.

Musical sound and noise are two broad types of sounds distinguished by the nature of their vibrations and how the ear/brain perceives them. Musical sounds arise from regular, periodic vibrations; they have a definite pitch, pleasant quality (timbre) and may be sustained or varied in a controlled way. Noise arises from irregular, aperiodic vibrations; it has no definite pitch and is generally perceived as unpleasant or disruptive.

Key characteristics:

• Pitch: Depends on frequency. Musical sounds have a definite pitch because they come from periodic vibrations (a clear frequency). Noise has no definite pitch because vibrations are irregular or contain many unrelated frequencies.
• Loudness: Depends on amplitude (energy) of the sound. Both musical sounds and noise can be loud or soft.
• Quality (timbre): Musical sounds usually contain a fundamental frequency plus harmonics (overtones) that give each instrument its characteristic tone. Noise has a broad, continuous mix of frequencies and lacks harmonic structure.
• Waveform: A pure musical tone is a simple sinusoid. Most musical instruments produce complex periodic waveforms (sum of harmonics). Noise produces random, non-repeating waveforms.

Why musical sound is pleasant and noise is not: The human auditory system recognises periodic patterns (harmonics) as structured sounds (notes, tones). Harmonic relationships (integer multiples of a fundamental) produce consonance and musical perception. Irregular, non-harmonic mixtures of frequencies are hard for the brain to organise and are perceived as noise.

Simple signal description (class-9 level): Musical sound: vibrations repeat regularly → definite frequency (f) and period (T = 1/f). Noise: vibrations do not repeat regularly → no single frequency defines it.

Effects and examples in daily life: Musical sound is used for communication, music, alarms with recognisable tones. Noise can disturb sleep, concentration, and may cause hearing loss if intense or prolonged.

Introduction
Sound enters the ear as pressure waves in air. The human ear converts these waves into nerve impulses that the brain interprets as sound. The ear has three main parts: outer ear, middle ear and inner ear — each with a specific role in collecting, amplifying and converting sound.

Parts of the ear and their functions

• Outer ear — Pinna (auricle) and external auditory canal. The pinna collects sound and helps determine direction; the canal funnels sound to the eardrum (tympanic membrane).
• Middle ear — Air-filled cavity containing the tympanic membrane and three ossicles (malleus, incus, stapes). The ossicles transmit and amplify vibrations from the eardrum to the oval window of the inner ear. The Eustachian tube equalizes pressure between the middle ear and throat.
• Inner ear — Fluid-filled cochlea and vestibular apparatus. The cochlea contains the basilar membrane and hair cells (sensory receptors). Vibrations at the oval window create pressure waves in cochlear fluid that move the basilar membrane. Moving hair cells convert mechanical motion to electrical signals sent via the auditory (cochlear) nerve to the brain.

Hearing mechanism — step by step

1. Sound wave in air reaches the outer ear and is guided down the ear canal to the tympanic membrane.
2. The eardrum vibrates with the same frequency as the incoming wave.
3. Vibrations are transferred to the ossicles. The ossicles act as a lever and, together with the smaller area of the stapes footplate, increase (match) pressure to transmit energy efficiently from air to cochlear fluid (impedance matching).
4. The stapes transmits vibrations to the oval window; this produces pressure waves in the cochlear fluid.
5. Pressure waves travel along the cochlea, causing a travelling wave on the basilar membrane. Different frequencies peak at different positions: high frequencies near the base, low frequencies near the apex (tonotopic arrangement).
6. Motion of the basilar membrane bends hair-cell stereocilia against the tectorial membrane, opening ion channels and generating receptor potentials.
7. Auditory nerve fibres fire action potentials whose pattern (frequency and place) encodes pitch and intensity; these signals go to auditory centres in the brain for interpretation.

Important additional points

• Frequency range: Typical human hearing ≈ 20 Hz to 20 kHz (range declines with age, especially at high frequencies).
• Intensity sensitivity: Threshold of hearing ~ 10^-12 W/m². Pain threshold ≈ 10²–10³ W/m² (around 120–130 dB).
• Protection: Acoustic reflex (stapedius and tensor tympani muscles) reduces transmission of very loud sounds; prolonged loud sounds damage hair cells leading to permanent hearing loss.
• Two conduction routes: Air conduction (normal route) and bone conduction (skull vibrations bypass outer/middle ear; basis of tuning-fork tests).

Simple diagram suggestions (to draw or show)

• Labelled cross-section of ear: pinna, ear canal, tympanic membrane, malleus, incus, stapes, oval window, round window, cochlea, basilar membrane, auditory nerve, Eustachian tube.
• Zoom-in of cochlea showing travelling wave on basilar membrane and hair cells at different positions for different frequencies.

Summary
The ear is a mechanical-to-hydraulic-to-electrical transducer: air pressure → mechanical motion (eardrum & ossicles) → fluid waves (cochlea) → electrical nerve signals (hair cells) → brain interpretation. Proper functioning and protection of each part are essential for clear hearing.

What is intensity?
Intensity of a sound wave is the power carried by the wave per unit area perpendicular to the direction of propagation. It tells how much energy arrives at a surface each second. Intensity is a physical, measurable quantity; loudness is the perceptual effect.

Key definitions and relations

• Intensity: I = P / A, where P is power (energy per second) delivered by the source and A is area (unit: W/m²).
• For a point source radiating uniformly in all directions: I = P / (4πr²). Intensity falls as the square of the distance (inverse-square law).
• For a given kind of wave, intensity is proportional to the square of the amplitude: I ∝ A². (If amplitude doubles, intensity increases fourfold.)
• Energy transported by sound in time t: E = P × t. (Energy is power multiplied by time.)

Perceptual effects — loudness and the decibel scale
Human perception of loudness is not linear with intensity. The ear responds approximately logarithmically: a large change in intensity is needed for a small perceived change in loudness. The sound level (SPL) in decibels is defined as:

L (dB) = 10 log₁₀(I / I₀), where I₀ = 1 × 10⁻¹² W/m² (threshold of hearing).

Important perceptual facts:

• 0 dB is near the threshold of hearing. 120–130 dB is near the threshold of pain.
• An increase of about 10 dB is generally perceived roughly as a doubling of loudness.
• Doubling the distance from a point source reduces intensity by a factor of four, which corresponds to about a −6 dB change (10 log₁₀(1/4) ≈ −6.02 dB).
• Pitch (frequency) is different from loudness: intensity affects loudness but not pitch.

Practical consequences
Because intensity decreases rapidly with distance, moving away from a noisy source is an effective way to reduce exposure. High intensities (high I or high dB) can damage hearing; many safety rules use decibel thresholds (e.g., long exposure above ~85 dB can cause hearing loss).

Short calculation examples (conceptual)
If a sound produces intensity I = 1 × 10⁻⁶ W/m² at a listener, its level is L = 10 log₁₀(1×10⁻⁶ / 1×10⁻¹²) = 10 log₁₀(10⁶) = 60 dB (typical conversation). If distance from a point source is doubled, intensity becomes one-fourth and level drops by ≈6 dB.

Summary
Intensity (W/m²) measures energy flux; energy = power × time. Loudness is how loud a sound seems and is related to intensity by a logarithmic decibel scale. Intensity depends on amplitude (I ∝ A²) and distance (I ∝ 1/r² for point sources).

Overview
This topic covers simple experiments and activities from the Class 9 chapter on Sound to demonstrate properties of sound (requires a medium, longitudinal nature, pitch & loudness, echo & reverberation, resonance) and how to solve numerical problems using the basic relations between speed, frequency and wavelength.

Key experiments & activities (what to do, observation, explanation)

• Bell in a glass jar (sound needs a medium)
  Method: Place a ringing bell inside a glass jar and remove the air with a vacuum pump. Observe the bell sound as air is slowly removed.
  Observation: Sound becomes fainter and finally almost inaudible as air is pumped out.
  Explanation: Sound is a mechanical wave and needs a material medium (air) to travel; with no air the sound cannot reach the ear.
• Vibrating tuning fork and resonance box (demonstrate vibration & amplification)
  Method: Strike a tuning fork and touch its stem to a wooden resonance box or place it over a table top. Compare loudness with/without the box.
  Observation: Sound becomes louder when the fork is in contact with the box.
  Explanation: The box increases the effective vibrating surface area and radiates sound more efficiently (larger amplitude → larger intensity).
• Slinky (show longitudinal waves, compressions & rarefactions)
  Method: Hold a slinky or spring on a table; one student gives short pushes along the spring axis to create pulses; observe particle motion and wave propagation.
  Observation: Regions of compression and rarefaction move along the spring while individual coils oscillate about fixed positions.
  Explanation: Sound in air is a longitudinal wave (particles oscillate parallel to wave propagation).
• Echo experiment (measure speed of sound using echo)
  Method: Stand at known distance from a large reflecting wall, create a sharp sound (clap) and measure time between sound and echo using a stopwatch or record and measure time. Alternatively, produce a sound near a wall and measure time taken to hear echo.
  Observation: Echo is heard after a time delay; using measured time t and distance d to wall, speed v = 2d / t.
  Explanation: The sound travels to the wall and back, so total distance = 2d; dividing by time gives speed.
• Resonance in an air column (find speed of sound)
  Method: Use a tube partly filled with water and a tuning fork of known frequency. Adjust water level (hence air column length L) until loud sound (resonance) is heard. For a tube closed at one end (open at top), the fundamental resonance condition: λ = 4L (approx).
  Observation: At resonance sound is amplified. Measure L, compute λ and then v = f·λ to get speed of sound.
  Note: For more accurate work add end-correction (L_eff = L + 0.3r, where r is tube radius).

Numerical problems — typical approach

Key relations: v = f·λ, f = 1/T, distance using echo d = v·t/2. Also speed variation with temperature: v_air( m/s ) = 331 + 0.6·T(°C) (approx).

Procedure for solving problems:

1. Identify known quantities (f, λ, time, distance, temperature).
2. Select relevant formula: v=fλ or d=(v·t)/2 etc.
3. Plug values (use consistent SI units) and solve stepwise, showing units.

Common practical notes

• Use approximate speed of sound in air at 20°C: 343 m/s (from v = 331 + 0.6·20).
• Echo is distinct only if the reflecting surface is at least about 17 m away (for ear to discriminate an echo); rule of thumb: sound must travel >0.1 s to the reflector and back for humans to hear a distinct echo.
• End correction matters for short tubes: effective length is slightly more than measured air column length.

Summary: Perform the listed experiments to observe the nature and properties of sound; use the formulas v = f·λ and d = v·t/2 to solve numerical problems. Always state assumptions (temperature for v, neglect end correction unless provided).