Sound

When an object vibrates, it causes the particles of the surrounding medium (such as air) to vibrate. These particles, in turn, cause their adjacent particles to vibrate, and this process continues outward.

This creates a series of alternating compressions (regions of high pressure where particles are crowded together) and rarefactions (regions of low pressure where particles are spread apart) that travel through the medium as a longitudinal wave.

When these pressure variations (compressions and rarefactions) reach the outer ear, they travel through the ear canal and cause the eardrum (tympanic membrane) to vibrate. This vibration is transmitted through the middle ear bones to the inner ear, where it is converted into nerve signals that the brain perceives as sound.

When the school bell is struck with a hammer, the metal of the bell starts vibrating rapidly (oscillating back and forth). This vibration disturbs the air particles immediately surrounding the bell.

As the bell surface moves outward, it pushes air particles together, creating a compression (high-pressure region). As it moves inward, it pulls the particles apart, creating a rarefaction (low-pressure region).

These alternating compressions and rarefactions travel outward through the air as a longitudinal sound wave, eventually reaching our ears and being perceived as the ringing of the bell. The sound continues as long as the bell continues to vibrate.

Sound waves are called mechanical waves because they require a material medium (solid, liquid, or gas) for their propagation. They cannot travel through vacuum.

Sound travels by the mechanical vibration of the particles of the medium. The particles pass on their kinetic energy (oscillation) to adjacent particles, creating a chain of disturbance through the medium. No particles actually travel from the source to the ear — only the mechanical disturbance (energy) travels.

This is in contrast to electromagnetic waves (like light, radio waves) which can travel through vacuum and do not require a medium.

No, you will not be able to hear any sound produced by your friend on the moon.

The moon has no atmosphere — it is essentially a vacuum. Sound is a mechanical wave that requires a material medium (solid, liquid, or gas) to propagate. Since there is no medium on the moon, sound waves cannot travel from your friend's mouth to your ears, no matter how loudly they shout.

Astronauts on the moon can only communicate through radio waves (electromagnetic waves), which do not require a medium and can travel through vacuum.

(a) Loudness is determined by the amplitude of the sound wave. The greater the amplitude of vibration, the louder the sound. Loudness is proportional to the square of amplitude. It is measured in decibels (dB).

(b) Pitch is determined by the frequency of the sound wave. The higher the frequency of vibration, the higher the pitch of the sound. For example, a whistle has a high pitch (high frequency) while a drum has a low pitch (low frequency).

The guitar has a higher pitch than a car horn.

A guitar produces musical notes at relatively high frequencies (typically hundreds of Hz, from about 82 Hz for the lowest string to over 1000 Hz for high notes). A car horn produces a comparatively lower frequency sound (typically around 300–500 Hz for the fundamental, but with a harsher, more blaring quality). In general musical context, guitar strings produce notes that are perceived as higher-pitched than a car horn's blaring sound. Higher frequency = higher pitch.

Wavelength (λ): The distance between two consecutive compressions or two consecutive rarefactions in a sound wave. It is the distance over which one complete cycle of the wave occurs. Unit: metre (m).

Frequency (n or f): The number of complete vibrations (oscillations) produced per second. Unit: hertz (Hz). 1 Hz = 1 vibration per second.

Time Period (T): The time taken to complete one full vibration or oscillation. It is the reciprocal of frequency:

Unit: second (s).

Amplitude (A): The maximum displacement of the medium particles from their undisturbed (mean/equilibrium) position when a sound wave passes through them. Amplitude determines the loudness of sound. Unit: metre (m).

The speed of sound is related to its frequency and wavelength by the wave equation:

where v = speed of sound (m/s), n = frequency (Hz), λ = wavelength (m).

The speed of sound in a given medium at a given temperature is constant. Therefore:

• If frequency increases, wavelength decreases proportionally (and vice versa).

• Speed of sound in air at 20°C ≈ 344 m/s. It increases with temperature.

This relationship means frequency and wavelength are inversely proportional when speed is fixed:

Given: Frequency n = 220 Hz, Speed v = 440 m/s.

The wavelength of the sound wave is 2 metres.

Given: Frequency n = 500 Hz.

The time interval between two successive compressions is the time period of the wave (the time for one complete vibration).

The time interval between successive compressions is 0.002 seconds (2 milliseconds). Note: the distance of 450 m is not needed for this calculation — the time period depends only on the frequency of the source.

Intensity of Sound: An objective, physical measure of the amount of sound energy flowing per unit area per unit time (power per unit area). It depends on the square of amplitude (I ∝ A²). Unit: watt per square metre (W/m²). It does not depend on the observer.

Loudness of Sound: A subjective sensation perceived by the human ear. It depends on both the intensity and the frequency of the sound. Sounds of the same intensity but different frequencies are perceived as having different loudness. Loudness is measured in decibels (dB).

Key difference: Intensity is a physical property of the wave; loudness is the subjective human perception of that intensity.

Sound travels fastest in iron (solid), then in water (liquid), and slowest in air (gas).

Approximate speeds of sound:

Sound travels fastest in solids because the particles in a solid are most tightly packed (strongest intermolecular forces), so they can transmit vibrations more readily. Gases have the loosest packing, resulting in the slowest sound transmission.

Given: Time for echo t = 3 s, Speed of sound v = 342 m/s.

The sound travels from the source to the reflecting surface and back, so it covers twice the distance.

The reflecting surface is 513 metres away from the source.

Note: For an echo to be heard separately from the original sound, the minimum distance of the reflecting surface should be about 17.2 m (so that the echo arrives at least 0.1 s after the original sound).

The ceilings of concert halls are curved (concave) so that sound after reflection from the ceiling reaches all parts of the hall uniformly.

A curved (concave) ceiling acts as a large curved reflector. When sound from the stage strikes the curved ceiling, it is reflected in such a way that it spreads evenly throughout the hall. This ensures:

(i) People sitting in all parts of the hall — front, back, sides — can hear the sound with adequate loudness.

(ii) No “dead spots” (areas of very low sound intensity) or echoes that would distort the sound.

Similarly, curved reflectors are placed behind the stage (at the back of the speaker's podium) to direct sound toward the audience. This application uses the principle of reflection of sound.

SONAR stands for Sound Navigation And Ranging. It is a device/technique that uses ultrasonic waves (frequency > 20,000 Hz) to detect and locate objects underwater.

Principle: Ultrasonic pulses are emitted from a transmitter on a ship or submarine. These waves travel through water at high speed, reflect (echo) off underwater objects, and return to a receiver. By measuring the time interval between sending and receiving the echo, the distance of the object is calculated:

where d = distance to object, v = speed of sound in water (≈ 1500 m/s), t = time for echo to return.

Uses of SONAR:

(i) Detecting enemy submarines, mines, and icebergs.

(ii) Measuring the depth of oceans (echo depth sounding).

(iii) Locating shoals of fish for fishermen.

(iv) Underwater navigation and mapping of the ocean floor.

(v) Detecting wrecks and underwater geological structures.

Given: Distance d = 3625 m, Time for echo t = 5 s.

Total distance covered by sound (to object and back) = 2d = 2 × 3625 = 7250 m.

The speed of sound in water is 1450 m/s.

This technique is called ultrasonic testing or non-destructive testing (NDT). It works as follows:

(i) A transmitter is placed on the surface of the metal block and sends ultrasonic waves into the metal.

(ii) These high-frequency waves travel through the metal block.

(iii) If the metal is uniform (no defects): the waves travel through without obstruction and only produce an echo from the far end of the block.

(iv) If there is a crack, cavity, or internal defect: the ultrasonic waves reflect back from the defect before reaching the far end. This early echo is detected by a receiver.

(v) By measuring the time and location of the early echo, the position and size of the defect can be precisely determined, all without damaging the metal block.

This method is widely used in manufacturing, aviation, and construction to ensure structural integrity of metal components.

The average human ear can hear sounds in the frequency range of 20 Hz to 20,000 Hz (20 kHz). This is called the audible range.

Infrasound: Sound with frequency below 20 Hz. Humans cannot hear it, but some animals (elephants, whales) can produce and detect infrasound.

Ultrasound: Sound with frequency above 20,000 Hz (20 kHz). Humans cannot hear it, but bats, dolphins, and dogs can. Ultrasound has many applications (SONAR, medical imaging, NDT).

Note: The upper limit of hearing decreases with age. Young children can hear up to 20 kHz, but older adults may only hear up to 15 kHz or less.