Question

What is the wavelength of the sound produced by a bat if the frequency of the sound is 90 kHz on a night when the air temperature is 22°C?

Answer 1

We know that the wavelength is related to the speed of the wave by:

`v=\lambda f`

where f is the frequency.

The speed of sound on air at a given temperature is given by:

`v=331\sqrt[]{1+(T)/(273)}`

so in this case the speed is:

`v=331\sqrt[]{1+(22)/(273)}=344.08`

Plugging this and the frequency in the first expression above we have:

`\begin{gathered} 344.08=90*10^3\lambda \\ \lambda=(344.08)/(90*10^3) \\ \lambda=3.82*10^(-3) \end{gathered}`

Therefore the wavelength is:

`3.82*10^(-3)\text{ m}`