Sound and Waves: Properties, Speed and PYQs

A wave is a disturbance that carries energy from one place to another without carrying matter with it. The particles of the medium only vibrate about their own positions; it is the energy, and not the material, that travels. Sound is the most examined example, and almost every question on this chapter comes back to one of three things: the nature of the wave, the relation between speed, frequency and wavelength, or the behaviour of sound when it is reflected.

Types of waves

Waves are first divided into mechanical waves, which need a material medium, and electromagnetic waves such as light and radio waves, which travel through vacuum. They are divided again by the direction of vibration. In a transverse wave the particles vibrate at right angles to the direction of travel, producing crests and troughs, as on the surface of water or in a stretched string. In a longitudinal wave the particles vibrate along the direction of travel, producing compressions where the particles crowd together and rarefactions where they spread out. Sound is a longitudinal mechanical wave, which is why it cannot pass through a vacuum. In the classic bell jar demonstration, an electric bell inside a jar becomes inaudible as the air is pumped out, although it can still be seen ringing.

Describing a wave

The distance between two consecutive compressions, or two consecutive crests, is the wavelength. The number of complete waves passing a point in one second is the frequency, measured in hertz, and the time taken for one complete wave is the time period, which is simply the reciprocal of the frequency. The maximum displacement of a particle from its rest position is the amplitude. The three quantities are tied together by one formula that papers use again and again: speed equals frequency multiplied by wavelength. Since the speed of sound in a given medium at a given temperature is fixed, a higher frequency must mean a shorter wavelength.

Speed of sound

Sound travels fastest in solids, more slowly in liquids and slowest in gases, because the particles of a solid are closely packed and pass the disturbance on quickly. In air at room temperature it moves at roughly three hundred and forty metres per second, in water at about fifteen hundred, and in steel at around five thousand. The speed rises as the temperature of the air rises and also rises slightly with humidity, because moist air is less dense than dry air. It does not change with a change in pressure alone, and it does not depend on the loudness or the pitch of the sound. Light, by contrast, travels at three hundred thousand kilometres per second, which is why lightning is seen well before thunder is heard.

Characteristics of a musical sound

Audible range, infrasound and ultrasound

The human ear normally responds to frequencies between about twenty hertz and twenty thousand hertz. Sound below twenty hertz is called infrasonic; elephants, whales and rhinoceroses use it, and it is produced before earthquakes and by volcanic activity. Sound above twenty thousand hertz is ultrasonic; bats, dolphins and porpoises produce and hear it, and dogs can hear far above the human limit. Ultrasound has a long list of uses, among them ultrasonography of the abdomen and the foetus, echocardiography of the heart, cleaning parts of machines that cannot be reached, detecting cracks and flaws inside metal castings, and breaking kidney stones.

Reflection of sound

Sound obeys the laws of reflection just as light does. The repetition of a sound by reflection from a distant surface is an echo. The sensation of a sound persists in the human brain for about a tenth of a second, so the reflected sound must arrive at least that much later to be heard separately. With sound travelling at about three hundred and forty-four metres per second, the reflecting surface must be at least about seventeen metres away. Repeated reflection in a closed hall causes the sound to persist as reverberation, which is reduced by covering the ceiling and walls with absorbing materials such as fibre board, curtains and carpets. Multiple reflection is put to work in the megaphone, the horn, the trumpet and the stethoscope, and the curved ceilings of concert halls are shaped so that reflected sound spreads evenly.

SONAR and the human ear

SONAR stands for Sound Navigation and Ranging. A transmitter on a ship sends out ultrasonic pulses, the pulses strike the sea bed, a submarine or a shoal of fish, and a detector picks up the echo. Since the pulse covers the distance twice, the depth is found by multiplying the speed of sound in water by the time taken and dividing by two. In the human ear, the outer ear collects sound and passes it to the eardrum, three small bones called the hammer, the anvil and the stirrup amplify the vibrations, and the coiled cochlea converts them into electrical signals that the auditory nerve carries to the brain.