17.2 Speed of sound  (Page 4/6)

The equation for the speed of sound in air $v=\sqrt{\frac{\gamma RT}{M}}$ can be simplified to give the equation for the speed of sound in air as a function of absolute temperature:

One of the more important properties of sound is that its speed is nearly independent of the frequency. This independence is certainly true in open air for sounds in the audible range. If this independence were not true, you would certainly notice it for music played by a marching band in a football stadium, for example. Suppose that high-frequency sounds traveled faster—then the farther you were from the band, the more the sound from the low-pitch instruments would lag that from the high-pitch ones. But the music from all instruments arrives in cadence independent of distance, so all frequencies must travel at nearly the same speed. Recall that

In a given medium under fixed conditions, v is constant, so there is a relationship between f and $\lambda ;$ the higher the frequency, the smaller the wavelength ( [link] ).

The speed of sound can change when sound travels from one medium to another, but the frequency usually remains the same. This is similar to the frequency of a wave on a string being equal to the frequency of the force oscillating the string. If v changes and f remains the same, then the wavelength $\lambda$ must change. That is, because $v=f\lambda$ , the higher the speed of a sound, the greater its wavelength for a given frequency.