Tuesday, March 3, 2015

Waves

Waves

Introduction to Waves

Wave motion is a travelling disturbance through a medium or through space, in which energy is transferred from one point to another without movement of matter.

Examples where wave motion occurs include:

(i) water waves, such as are produced when a stone is thrown into a still pool of water

(ii) waves on strings

(iii) waves on stretched springs

(iv) sound waves

(v) light waves (see page 75)

(vi) radio waves

(vii) infra-red waves, which are emitted by hot bodies

(viii) ultra-violet waves, which are emitted by very hot bodies and some gas discharge lamps

(ix) x-ray waves, which are emitted by metals when they are bombarded by high speed electrons

(x) gamma-rays which are emitted by radioactive elements.

Examples (i) to (iv) are mechanical waves and they require a medium (such as air or water) in order to move. Examples (v) to (x) are electromagnetic waves and do not require any medium — they can pass through a vacuum.

Wave Types

There are two types of waves, these being transverse and longitudinal waves:

(i) Transverse waves are where the particles of the medium move perpendicular to the direction of movement. For example, when a stone is thrown onto a pool of still water, the ripple moves radially outwards but the movement of a floating object shows that the water at a particular point merely moves up and down. Light and radio waves are other examples of transverse waves.

(ii) Longitudinal waves are where the particles of the medium vibrate back and forth parallel to the direction of the wave travel. Examples include sound waves and waves in springs.

Figure 17.1 shows a cross section of a typical wave.

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Wavelength, Frequency and Velocity

Wavelength is the distance between two successive identical parts of a wave (for example, between two crests as shown in Figure 17.1). The symbol for wavelength is A (Greek lambda) and its unit is metres.

Frequency is the number of complete waves (or cycles) passing a fixed point in one second. The symbol for frequency is f and its unit is the hertz, Hz.

The velocity, v of a wave is given by:

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The unit of velocity is metres per second.

For example , if BBC radio 4 is transmitted at a frequency of 198 kHz and a wavelength of 1500 m, the velocity of the radio wave v is given by:

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Reflection and Refraction

Reflection is a change in direction of a wave while the wave remains in the same medium. There is no change in the speed of a reflected wave. All waves are reflected when they meet a surface through which they cannot pass. For example,

(i) light rays are reflected by mirrors,

(ii) water waves are reflected at the end of a bath or by a sea wall,

(iii) sound waves are reflected at a wall (which can produce an echo),

(iv) a wave reaching the end of a spring or string is reflected, and

(v) television waves are reflected by satellites above the Earth.

Experimentally, waves produced in an open tank of water may readily be observed to reflect off a sheet of glass placed at right angles to the surface of the water.

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Refraction is a change in direction of a wave as it passes from one medium to another. All waves refract, and examples include:

(i) a light wave changing its direction at the boundary between air and glass, as shown in Figure 17.2,

(ii) sea waves refracting when reaching more shallow water, and

(iii) sound waves refracting when entering air of different temperature (see below).

Experimentally, if one end of a water tank is made shallow the waves may be observed to travel more slowly in these regions and are seen to change direction as the wave strikes the boundary of the shallow area. The greater the change of velocity the greater is the bending or refraction.

Sound Waves and their Characteristics

A sound wave is a series of alternate layers of air, one layer at a pressure slightly higher than atmospheric, called compressions, and the other slightly lower, called rarefactions. In other words, sound is a pressure wave. Figure 17.3(a) represents layers of undisturbed air; Figure 17.3(b) shows what happens to the air when a sound wave passes.

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Sound waves exhibit the following characteristics:

(i) Sound waves can travel through solids, liquids and gases, but not through a vacuum.

(ii) Sound has a finite (i.e. fixed) velocity, the value of which depends on

the medium through which it is travelling. The velocity of sound is also affected by temperature. Some typical values for the velocity of sound are: air 331 m/s at 0°C, and 342 m/s at 18° C, water 1410 m/s at 20°C and iron 5100 m/s at 20°C.

(iii) Sound waves can be reflected, the most common example being an echo.

Echo-sounding is used for charting the depth of the sea.

(iv) Sound waves can be refracted. This occurs, for example, when sound waves meet layers of air at different temperatures. If a sound wave enters

a region of higher temperature the medium has different properties and the wave is bent as shown in Figure 17.4, which is typical of conditions

that occur at night.

Sound waves are produced as a result of vibrations.

(i) In brass instruments, such as trumpets and trombones, or wind instruments, such as clarinets and oboes, sound is due to the vibration of columns of air.

(ii) In stringed instruments, such as guitars and violins, sound is produced by vibrating strings causing air to vibrate. Similarly, the vibration of vocal chords produces speech.

(iii) Sound is produced by a tuning fork due to the vibration of the metal prongs.

(iv) Sound is produced in a loudspeaker due to vibrations in the cone.

The pitch of a sound depends on the frequency of the vibrations; the higher the frequency, the higher is the pitch. The frequency of sound depends on the form of the vibrator. The valves of a trumpet or the slide of a trombone lengthen or shorten the air column and the fingers alter the length of strings on a guitar or violin. The shorter the air column or vibrating string the higher the frequency and hence pitch. Similarly, a short tuning fork will produce a higher pitch note than a long tuning fork.

The human ear can perceive frequencies between about 20 Hz and 20 kHz.

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