Chapter 10: Sound Waves: Characteristics and Applications

Every sound begins with a vibration, a rapid to and fro motion of an object. The object that vibrates is the source. In a tabla the stretched membrane vibrates, in a sitar the strings, in a bansuri the air column inside the pipe, and in humans the vocal cords inside the larynx. A tuning fork is struck on a soft rubber pad so that its prongs vibrate. When the vibration stops, the sound stops too. Most instruments have more than one vibrating part, and the body of the instrument makes the sound fuller.

Sound travels from a source to a listener through a medium, which can be a solid, a liquid or a gas. A space with no matter is a vacuum. In the bell jar experiment an electric bell keeps ringing inside a sealed jar while the air is pumped out, and the sound grows fainter and finally cannot be heard, although the bell is still seen vibrating. Letting the air back in brings the sound back. This shows that sound cannot travel in a vacuum. Light does not need a medium, which is why sunlight reaches the Earth but no sound comes from the Sun. Astronauts in space communicate with devices fitted in their suits.

A sound wave is a series of compressions and rarefactions moving through a medium. A compression is a region where the particles are crowded and the density is higher than average, and a rarefaction is a region where they are spread out and the density is lower. The particles do not travel with the wave; each vibrates about its mean position parallel to the direction of the wave, so sound is a longitudinal wave. In a transverse wave the particles vibrate at right angles to the direction of travel, as in light. Sound is also a mechanical wave because it needs a medium. A moving piston makes a compression as it goes forward and a rarefaction as it comes back.

A wave can be described with a few measurable quantities. The distance between two consecutive crests or two consecutive troughs is the wavelength, measured in metres. The number of density oscillations at a fixed point in one second is the frequency ν, measured in hertz, where 1 Hz is one oscillation per second. The time for one complete oscillation is the time period T, measured in seconds. The two are inversely related by ν = 1 / T. On a density graph, the highest point is a crest, which marks a compression, and the lowest point is a trough, which marks a rarefaction. A pure single-frequency sound is called a tone.

A vibrating source passes energy to the medium, and a sound wave carries that energy, not the particles, from one place to another. The amplitude is the maximum change in density from the average. A larger amplitude carries more energy and is heard louder. The intensity is the amount of sound energy passing through a unit area in one second. Intensity falls with distance because the same energy spreads over a larger area. A microphone converts sound into an electrical signal, and a loudspeaker converts an electrical signal into sound. A hearing aid has a microphone, an amplifier and a speaker.

The speed of sound is the distance travelled by a point on the wave, such as a crest, in one second. For any wave, v = λ × ν. Sound travels fastest in solids, slower in liquids and slowest in gases. In dry air it is about 331 m/s at 0 °C and about 344 m/s at 22 °C, so it increases with temperature, and also with humidity. In most media the speed depends on the medium and not on the frequency, so if the frequency rises the wavelength falls. Sound is about 1500 m/s in sea water and about 5000 m/s in steel. Light is far faster than sound, so lightning is seen before the thunder is heard.

Pitch is how the ear perceives frequency, so a high-frequency sound is shrill and a low-frequency sound is deep. Loudness depends on amplitude and is measured in decibels, written dB. The audible range of a human is about 20 Hz to 20 kHz. Waves below 20 Hz are infrasonic, felt by elephants, and above 20 kHz are ultrasonic, heard by dogs, bats and dolphins. Unwanted sound is noise. The eardrum vibrates and the cochlea turns the vibrations into signals for the brain. Two instruments can play the same note at the same loudness and still sound different because of timbre. An octave is a note of double the frequency.

When a sound strikes a hard surface it bounces back, which is reflection of sound, and the angle of incidence equals the angle of reflection. A repeated sound heard after reflection is an echo. The ear holds a sound for about 0.1 s, so the reflected sound must come back at least 0.1 s later, which needs a surface about 17 m away when the speed is 340 m/s. Persistence of sound from repeated reflections is reverberation, reduced by soft materials. Ultrasound is used in medical scans, cleaning and finding cracks. Bats and dolphins find their way by echolocation, and ships use SONAR to find depth, where distance is half of speed × time.