Sound

Every sound we hear starts with something vibrating — moving rapidly to and fro about a fixed position. When you pluck a guitar string, strike a tabla, or speak, the string, the drum membrane, or your vocal cords vibrate rapidly. These vibrations disturb the particles of the medium (usually air) touching the vibrating body.

A vibrating particle does not travel all the way to your ear by itself. Instead, it pushes the neighbouring particles, which push the next ones, and so on. Each particle vibrates about its own mean position and passes the disturbance forward, carrying energy but not matter. This travelling disturbance is called a sound wave.

In air, the particles vibrate parallel to the direction in which the sound travels. Such a wave is called a longitudinal wave. As the vibrating source moves forward, it pushes air particles closer together, creating a region of high pressure and high density called a compression (C). As it moves back, it creates a region of low pressure and low density called a rarefaction (R). A sound wave is really a series of compressions and rarefactions travelling one after another through the medium.

Worked example: A bell is rung inside a glass jar connected to a vacuum pump. Initially, with air inside the jar, the ringing is heard clearly. As air is pumped out, the sound becomes fainter and fainter, and once almost all the air is removed, no sound is heard at all — even though the hammer can still be seen striking the bell through the glass. This shows that sound needs a material medium (solid, liquid or gas) to travel, and it cannot travel through vacuum. This is also why astronauts on a spacewalk cannot talk to each other directly through the vacuum of space and must use radio signals instead.

Just like any wave, a sound wave can be described completely using a few measurable quantities.

Wavelength (λ): The distance between the centres of two consecutive compressions or two consecutive rarefactions is called the wavelength. It is measured in metres (m).

Frequency (f or ν): The number of complete oscillations (or the number of compressions, or the number of rarefactions) produced per second is the frequency of the sound wave. Its SI unit is the hertz (Hz); 1 Hz means one complete vibration per second. Frequency decides the pitch of a sound — a high-frequency sound has a high (shrill) pitch, and a low-frequency sound has a low (grave) pitch.

Time period (T): The time taken to complete one full oscillation (one compression plus one rarefaction) is the time period. It is the reciprocal of frequency.

Amplitude (A): The maximum displacement of the particles of the medium from their mean (rest) position, on either side, is called the amplitude of the wave. A larger amplitude makes the sound louder; a smaller amplitude makes it softer. Amplitude does not change the pitch.

Speed (v): The distance travelled by the wave in one second is its speed, measured in m/s. Speed, frequency and wavelength are connected by one of the most useful relations in this chapter:

v = f × λ

Worked example: A sound wave has a frequency of 2 kHz (2000 Hz) and a wavelength of 35 cm (0.35 m) in a certain medium. Find its speed, and the time it will take to travel a distance of 1.5 km.

Speed: v = f × λ = 2000 Hz × 0.35 m = 700 m/s.

Time to travel 1.5 km (1500 m): time = distance ÷ speed = 1500 m ÷ 700 m/s ≈ 2.14 s.

The speed of sound depends on the medium through which it travels. Since sound propagates by particles colliding with their neighbours, it travels fastest where particles are packed closely together and are strongly linked — that is, in solids. It travels slower in liquids, and slowest in gases, where particles are far apart.

In general: speed of sound in solids > speed of sound in liquids > speed of sound in gases.

For example, sound travels at about 346 m/s in air at 25°C (often approximated as 340–344 m/s in numerical problems), about 1493 m/s in water at 25°C, and about 5960 m/s in steel — these are the standard reference values used in the NCERT speed-of-sound table. The speed of sound in a gas such as air also increases as the temperature of the gas increases, because warmer particles vibrate faster and transfer the disturbance more quickly.

The human ear is not able to detect every frequency of sound. A healthy young person can normally hear sound with frequencies from about 20 Hz to 20,000 Hz (20 kHz). This range is called the audible range of hearing.

Sound waves with a frequency below 20 Hz are called infrasonic sound (or infrasound). Humans cannot hear these, but animals like elephants, rhinoceroses and whales produce and use infrasound to communicate over long distances, and such very low-frequency vibrations are also associated with events like earthquakes.

Sound waves with a frequency above 20,000 Hz are called ultrasonic sound (or ultrasound). Bats and dolphins can produce and detect ultrasound; bats use it to locate obstacles and prey in the dark, a technique called echolocation.

Worked example: A dog can hear sound of frequency 25,000 Hz, but a human standing next to it cannot. Since the human audible range is only up to about 20,000 Hz, a frequency of 25,000 Hz lies in the ultrasonic range, above the upper limit of human hearing. A dog's audible range extends higher than a human's, so the dog can detect it while the human cannot.

Like light, sound also bounces back when it strikes a large, hard surface, such as a wall, a cliff, or a hillside. This is called reflection of sound, and it obeys the same laws as the reflection of light:

• The angle of incidence is equal to the angle of reflection.
• The incident sound wave, the reflected sound wave, and the normal at the point of incidence all lie in the same plane.

When a reflected sound reaches a listener late enough to be heard as a separate, repeated sound (rather than blending with the original), it is called an echo. This happens because the human ear keeps sensing a sound for about 0.1 second after the source stops (this is called the persistence of hearing). So, for an echo to be heard distinctly, the reflected sound must reach the ear at least 0.1 s after the original sound.

This sets a minimum distance between the source/listener and the reflecting surface. If v is the speed of sound, the sound must travel to the surface and back (a distance of 2d, where d is the distance to the surface) in at least 0.1 s.

Worked example: Taking the speed of sound in air as 344 m/s, find the minimum distance of a reflecting surface from a source so that an echo can be heard distinctly.

Total distance travelled by sound (to the surface and back) = v × t = 344 m/s × 0.1 s = 34.4 m.

Minimum distance of the surface, d = 34.4 m ÷ 2 = 17.2 m.

So the reflecting surface must be at least about 17.2 m away for a distinct echo to be heard in air.

In large halls or auditoriums, sound reflects again and again off the walls, ceiling and floor before dying out, causing the original sound to persist and become blurred — this is called reverberation. Excessive reverberation is reduced by covering the walls and ceiling with sound-absorbent materials such as compressed fibreboard, rough plaster, or heavy curtains.

Ultrasound is sound of frequency greater than 20,000 Hz — too high for humans to hear, but extremely useful because it travels in narrow, well-defined beams and can carry a lot of energy.

Some common uses of ultrasound:

• Cleaning hard-to-reach parts of objects such as spiral tubes and odd-shaped machine parts: objects are placed in a cleaning solution, and ultrasonic waves are passed through the solution to dislodge dirt and grease particles without damaging the object.
• Detecting cracks and flaws inside metal blocks used in structures and machines, which are otherwise invisible from the outside; ultrasonic waves pass through the metal and are reflected back by any flaw, revealing its presence and position.
• In medicine, ultrasound is used to obtain images of internal organs (ultrasonography), to examine the heart (echocardiography), and to break down kidney stones into fine grains without surgery.
• In SONAR (SOund Navigation And Ranging), a ship or submarine sends out ultrasonic waves and detects the echo reflected from an object underwater, such as the sea bed, a shoal of fish, or another vessel. Measuring the time taken for the echo to return allows the distance of the object to be calculated, since the reflected wave travels the distance to the object and back.

Worked example: A SONAR device on a ship sends an ultrasonic signal that returns as an echo from the sea bed after 2 s. If the speed of sound in sea water is 1500 m/s, find the depth of the sea at that point.

Total distance travelled by the signal (down to the sea bed and back up) = v × t = 1500 m/s × 2 s = 3000 m.

Depth of the sea, d = 3000 m ÷ 2 = 1500 m.

The human ear receives sound waves and converts them into electrical signals the brain can interpret. It has three main parts:

• Outer ear: the visible part (pinna) collects sound waves from the surroundings and funnels them through the auditory canal to the eardrum (tympanic membrane), which vibrates back and forth.
• Middle ear: contains three small, delicate bones — the hammer, anvil and stirrup — joined end to end. These bones amplify the vibrations of the eardrum and pass them on to the inner ear.
• Inner ear: the vibrations enter a coiled, fluid-filled structure called the cochlea, which converts the pressure vibrations into electrical signals. These signals travel through the auditory nerve to the brain, which interprets them as sound.