Speed of Sound
The transmission of energy by propagation of waves is one of the most common phenomena which we experience. Our lives would be radically different if we could not communicate with each other readily through the use of sound waves. Life would be impossible if it were not for the energy coming to the Earth from the Sun in the form of electromagnetic waves. While the effects of waves can be intriguing and sometimes beautiful, as in the case of light wave phenomena, all waves share characteristics which can be better understood by studying sound waves. In particular, all sound and light waves are oscillatory phenomena, and so they both have the characteristic of frequency, the number of cycles or oscillations per second, commonly expressed in the unit hertz (Hz). The waves propagate with characteristic speeds. All light, regardless of frequency (or color), propagates in the absence of matter with a speed of approximately 3.00 x 108 m/s. When passing through matter, the speed of light depends both on the nature of the material and on the frequency of the light. Sound also propagates with a speed which depends on the nature of the material through which the sound is passing, but to a high degree, the speed of the sound is independent of the frequency f, of the sound. A person’s voice is made up of sounds of different frequencies uttered simultaneously. If these different components did propagate at different speeds, a person’s voice would sound different if the person speaking were close to us rather than far away. Far away, the more slowly moving sound components would reach us later than the faster moving ones, and a word spoken at a distance would sound slurred and of variable pitch. For sound in dry air at 0° C the speed of sound is about 332 m/s. Since changes in temperature affect gases readily, the medium changes according to the temperature, and one can show that over the normal range of temperature of air, the speed of sound in dry air at a Celsius temperature t is given by the expression
v(t) = 332(1+ t/546)m/s . (1)
The period T, the time required for a wave to complete one whole cycle, is just the inverse of the frequency; T, equals 1/f. The distance which the wave travels in a single period is called the wavelength, λ, and so λ equals the product of the period T and the speed v, vT. Replacement of T by 1/f and rearrangement gives the fundamental relation
v = λf . (2)
Another important property which all waves have in common is that of resonance. When the waves are in a cavity of a particular size, the wave will reflect from the walls of the cavity and the reflected wave can interact with the original wave to augment or to diminish it. This is called, respectively, constructive or destructive interference and is responsible for standing waves similar to those observed on strings. This wave phenomenon is important in giving musical instruments their characteristic tones or pitches. It is possible to use a source of sound of known frequency and the standing wave pattern created by the resonance phenomenon to determine the wavelength of the sound. Using Eq. (2) an experimental value vexp, for the speed of sound can be obtained. This measured value of v can then be compared with the theoretical value vtheo, given by Eq. (1).
When a source of sound, such as a vibrating tuning fork, is held at the end of a tube, the sound wave will propagate to the other end of the tube and be reflected. This reflection is different if the tube is closed at the far end than if it is open. In either case, the reflected wave usually will interfere destructively with the original wave, and the sound in the tube is diminished. However at certain characteristic lengths, related…