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?

Respuesta :

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

[tex]v=\lambda f[/tex]

where f is the frequency.

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

[tex]v=331\sqrt[]{1+\frac{T}{273}}[/tex]

so in this case the speed is:

[tex]v=331\sqrt[]{1+\frac{22}{273}}=344.08[/tex]

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

[tex]\begin{gathered} 344.08=90\times10^3\lambda \\ \lambda=\frac{344.08}{90\times10^3} \\ \lambda=3.82\times10^{-3} \end{gathered}[/tex]

Therefore the wavelength is:

[tex]3.82\times10^{-3}\text{ m}[/tex]