Question

A bat can detect small objects such as an insect whose size is approximately equal to the wavelength of the sound the bat makes. What is the smallest insect a bat can detect? Assume that bats emit a chirp at a frequency of 47.6 kHz, and that the speed of sound in air is 413 m/s. Answer in units of mm.

Answer 1

Given that,

Frequency emitted by the bat, f = 47.6 kHz

The speed off sound in air, v = 413 m/s

We need to find the wavelength detected by the bat. The speed of a wave is given by formula as follows :

$v=f\lambda\\\\\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{413}{47.6\times 10^3}\\\\\lambda=0.00867\ m$

or

$\lambda=8.67\ mm$

So, the bat can detect small objects such as an insect whose size is approximately equal to the wavelength of the sound the bat makes i.e. 8.67 mm.