Question

Bats can detect small objects such as insects that are of a size on the order of a wavelength. if bats emit a chirp at a frequency of 69.3 khz and the speed of sound waves in air is 330 m/s, what is the smallest size insect they can detect? give your answer in mm (millimeters)

Answer 1

The smallest size of the insect that the bats can detect corresponds to the wavelength of the chirp they emit.

Their chirp has a frequency of
$f=69.3 kHz=69.3 \cdot 10^3 Hz$
and the speed of the chirp is equal to the speed of sound in air:
$v=330 m/s$
Therefore the wavelength of the chirp is
$\lambda= \frac{v}{f}= \frac{330 m/s}{69.3 \cdot 10^3 Hz}=4.76 \cdot 10^{-3} m$
which corresponds to a size of 4.76 mm.