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