Waves and Sound

Drop a pebble in a still pond. A ring spreads outwards, but the water itself does not travel to the bank; a leaf on the surface just bobs up and down. That is the whole secret of a wave: it is a disturbance that carries energy from one place to another without carrying the medium with it. Sound, light, a Mexican wave in a stadium, the shaking of the ground in an earthquake: all are waves, and all of them move energy, not matter.

Waves are classified in two ways. By need of a medium: mechanical waves (sound, water waves, waves on a string) cannot move without a material medium, because they pass on the vibration from particle to particle; electromagnetic waves (light, radio, X-rays) need no medium and travel even in vacuum. By direction of vibration: in a transverse wave the particles vibrate at right angles to the direction the wave travels, forming crests and troughs; in a longitudinal wave the particles vibrate along the direction of travel, forming compressions and rarefactions.

The wave carries energy, not the medium. Each particle only oscillates about its mean position. That is why a cork on the sea moves up and down while the wave runs to the shore.

Now the vocabulary that every wave question uses. Amplitude (A) is the maximum displacement of a particle from its mean position; it decides how much energy the wave carries. Wavelength (λ) is the distance between two consecutive crests (or two consecutive troughs, or one compression and the next compression). Time period (T) is the time for one complete oscillation, and frequency (f) is the number of oscillations per second, so f = 1/T. The unit of frequency is the hertz (Hz), named after Heinrich Hertz. The speed of the wave is the distance a crest covers in one second.

Every wave, whether sound or light, shows four behaviours that exams love. Reflection: the wave bounces back from a surface. Refraction: the wave bends when it enters a new medium because its speed changes. Diffraction: the wave bends around an obstacle or spreads after passing through a narrow gap; it is strongest when the gap or obstacle is comparable to the wavelength. Interference: two waves meeting add up (constructive) or cancel (destructive). Remember that frequency never changes when a wave enters a new medium; only speed and wavelength change.

Put your fingers on your throat and hum. You can feel a buzz. Touch a ringing school bell and it trembles. Sound is produced by vibrating bodies: a vibrating vocal cord, a plucked string, a struck tuning fork, a beaten drum. The vibrating body pushes the air next to it, and this push is handed on from one layer of air to the next. Our ear catches the final push and the brain calls it sound.

Because sound is a mechanical, longitudinal wave, it needs a material medium (solid, liquid or gas). It cannot travel through a vacuum. This is why astronauts on the Moon, which has no air, talk to each other by radio (an electromagnetic wave) and not by shouting. In a gas or liquid the particles do not travel from the speaker to the listener; they only vibrate back and forth about their positions and pass on the pressure variation. Regions of higher pressure are compressions and regions of lower pressure are rarefactions.

Sound needs a medium, light does not. That single fact explains why we see lightning first and hear thunder later (light is far faster), and why there is no sound in outer space.

Speed of sound depends on the medium, not on the loudness or pitch of the sound. The general order is solids > liquids > gases. Why? Because in a solid the particles are packed tightly and are strongly linked, so a push passes on quickly; in a gas they are far apart and the push is slow to travel. In air at about 20 to 25 °C the speed is roughly 343 m/s (about 331 m/s at 0 °C). It rises with temperature, by roughly 0.6 m/s for each degree Celsius. For the same reason sound is faster in moist air than in dry air, and faster in hydrogen than in air.

What happens when sound crosses from one medium to another, say from air into water? The frequency stays the same, because the source fixes it. But the speed changes: in water it is about four to five times that in air. Since v = f λ and f is fixed, the wavelength also increases. Going from a solid to a gas does the reverse: the speed drops and the wavelength shortens. One historical detail: Newton gave a formula for the speed of sound assuming temperature stays constant; Laplace corrected it in 1816 by treating the compressions as adiabatic (no heat exchange).

Stand in front of a hill or a large empty hall and shout 'Radhika!'. A moment later you hear 'Radhika' coming back at you. Sound, like light, bounces off a hard surface, and it follows the same laws of reflection: the angle of incidence equals the angle of reflection, and the incident wave, reflected wave and the normal all lie in the same plane. Hard, smooth surfaces such as walls, cliffs and metal reflect sound well; soft surfaces such as curtains, carpets and cloth absorb it.

The returning sound is called an echo (प्रतिध्वनि). But you do not hear every reflection as an echo. Our brain holds on to a sound for about 0.1 second (persistence of hearing). If the reflected sound reaches the ear sooner than that, it merges with the original sound and no separate echo is heard. For a distinct echo the gap must be at least 0.1 s. Since the sound goes to the wall and back, the total path is 2d, so with speed about 344 m/s at 22 °C: 2d = 344 × 0.1, giving d ≈ 17.2 m (roughly 17 m) as the minimum distance between you and the reflector.

Reverberation is the persistence of sound in a closed hall because of repeated reflections from the walls, floor and ceiling, even after the source has stopped. A little reverberation makes music rich, but too much makes speech a muddle, because each word is smeared into the next. Engineers reduce it with sound-absorbing materials: heavy curtains, carpets, upholstered seats, perforated boards and rough plaster. Note that an echo is a separate, distinct repeat of the sound, whereas reverberation is a continuous, overlapping prolongation.

Sound's reflection is put to use in many places. A megaphone, bugle and horn send the sound in one direction by repeated reflection from the tube walls. A stethoscope guides the sound of the heartbeat to the doctor's ear. The ceilings of concert halls and cinemas are curved, and a curved soundboard is placed behind the speaker, so that reflected sound spreads to all corners. Bats and dolphins find prey by echolocation, and ships use SONAR. Thunder rolls because the sound is reflected again and again from clouds and the ground.

Two sounds can differ in three ways, and the exam asks all three. Pitch (तारत्व) tells how shrill or flat a sound is, and it depends on frequency: higher frequency, higher pitch. A girl's voice or a whistle has a high pitch; a lion's roar has a low pitch. Loudness (प्रबलता) tells how strong the sound feels to the ear, and it depends on the amplitude of vibration: larger amplitude, louder sound. Quality or timbre (गुणता) is what lets you tell a sitar from a flute playing the same note at the same loudness, and it depends on the waveform (the mixture of overtones).

The unit of loudness level is the decibel (dB), named after Alexander Graham Bell. It runs on a scale where the faintest sound a healthy ear can detect is about 0 dB, a whisper is about 30 dB, normal conversation about 60 dB, and a jet engine nearby well above 120 dB. Sounds above roughly 120 dB can be painful, and long exposure to high noise damages hearing and raises stress and blood pressure; this is noise pollution. In India the CPCB limits for residential areas are 55 dB by day and 45 dB by night.

Human beings hear frequencies from 20 Hz to 20,000 Hz (20 kHz); this is the audible range (श्रव्य). Below 20 Hz the sound is infrasonic (अवश्रव्य); above 20 kHz it is ultrasonic (पराश्रव्य). Children can hear up to a little above 20 kHz, and the upper limit falls with age. Other animals live in other ranges: elephants, whales and rhinoceroses use infrasound to talk over long distances; dogs, bats, dolphins and porpoises hear and produce ultrasound. Infrasound is produced by earthquakes, volcanic eruptions and ocean waves, and some animals sense it before an earthquake.

SONAR stands for SOund Navigation And Ranging. A transmitter on the ship sends an ultrasonic pulse down; it hits the sea-bed (or a submarine, or a shoal of fish) and an echo returns to the detector. If the echo comes back after time t and the speed of sound in sea water is v, the pulse has travelled to the object and back, so 2d = v × t. SONAR is used to find the depth of the sea, to map the sea-floor, and to locate submarines, sunken ships and fish. Ultrasound is preferred because its short wavelength gives a narrow beam that does not spread out much.

Finally, resonance (अनुनाद). Every object has a natural frequency at which it likes to vibrate. If a periodic push of the same frequency is applied, the vibrations pile up and the amplitude becomes very large. A child on a swing, pushed in step with its swing, goes higher and higher: that is resonance. The same effect makes a glass shatter when a singer hits its natural frequency, makes soldiers break step while crossing a bridge, brought down the Tacoma Narrows Bridge (USA, 1940), and lets us tune a radio to a station. Musical instruments use resonance in their hollow bodies (sitar's tumba, guitar's box) to boost the sound.

Stand on a railway platform as a fast train blows its whistle and rushes past. As it comes closer the whistle sounds shriller; the moment it crosses you, the pitch drops suddenly. The whistle itself has not changed, so why does your ear hear a different note? This is the Doppler effect, explained by the Austrian physicist Christian Doppler in 1842: *the apparent frequency of a wave changes when there is relative motion between the source and the observer.*

The reason is simple geometry. When the source moves towards you, it keeps catching up with its own waves, so successive crests get squeezed closer: wavelength shortens and you receive more crests per second, so the observed frequency rises (higher pitch). When the source moves away, the crests get stretched apart, fewer reach you per second, and the observed frequency falls (lower pitch). The source's own frequency never changes; only what the observer receives changes. The same happens if the observer moves towards or away from a stationary source.

The Doppler effect works for all waves, so it has many uses. Radar speed guns used by traffic police send radio waves at a moving car and read the shift in the reflected wave to find its speed. Doppler weather radar (used by the India Meteorological Department) tracks the motion of rain and storm clouds. Doppler ultrasound measures the speed of blood flow in the body. In astronomy, light from galaxies moving away is shifted to longer wavelengths (red shift), and from those moving towards us to shorter wavelengths (blue shift); the red shift of distant galaxies is the key evidence that the universe is expanding.

Now push the idea to the limit. What if the source moves faster than sound itself? The waves can no longer run ahead of it; they pile up into a cone-shaped shock wave (the Mach cone) trailing behind the object. When this cone sweeps over the ground we hear a sudden thunder-like sonic boom. The ratio of the object's speed to the speed of sound is the Mach number (named after Ernst Mach): Mach < 1 is subsonic, Mach = 1 is the speed of sound, Mach > 1 is supersonic, and above about Mach 5 it is hypersonic. At sea level, Mach 1 is about 1230 km/h (343 m/s). A listener hears the boom only after the supersonic aircraft has passed overhead.

Light, the radio signal that carries a cricket commentary, the heat from a bonfire and the X-ray in a hospital look like completely different things. Yet they are all members of one family: electromagnetic (EM) waves. In 1864 James Clerk Maxwell showed from his equations that a changing electric field produces a changing magnetic field and vice versa, so the two can keep each other going and travel through empty space as a self-sustaining wave. Heinrich Hertz produced such waves in the laboratory in 1887.

Arrange all EM waves in order of wavelength (or frequency) and you get the electromagnetic spectrum. From the longest wavelength (lowest frequency, lowest energy) to the shortest (highest frequency, highest energy), the order is: Radio waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, Gamma rays.

Two points that exams love. First, UV rays are divided into UV-A, UV-B and UV-C; the Sun emits all three, but the ozone layer absorbs the dangerous UV-C and most of UV-B, which is why ozone depletion is a worry (skin cancer and cataract). Second, the Sun's most intense radiation lies in the visible region, and the hotter an object is, the shorter the wavelength at which it radiates the most energy (Wien's displacement law). Also remember that the very first Nobel Prize in Physics (1901) went to W. C. Röntgen for X-rays.