Question

Female Aedes aegypti mosquitoes emit a buzz at about 4.00×102 Hz, whereas male A. aegypti mosquitoes typically emit a buzz at about 6.00×102 Hz. As a female mosquito is approaching a stationary male mosquito, is it possible that he mistakes the female for a male because of the Doppler shift of the sound she emits?

How fast would the female have to be traveling relative to the male for him to make this mistake? Assume the speed of sound in the air is 343 m/s.

Answer 1

When an approaching source moves closer to the stationary object, its apparent frequency increases due to Doppler Shift. So the formula for the Doppler shift is

where V is the speed of sound in air, Vs is the speed of the approaching female mosquito, f is the frequency of the buzz emitted by the female mosquito, and f' is the apparent frequency heard by the male mosquito. So it is possible that a stationary male mosquito mistakes the female for a male if she approaches fast enough. We need to calculate the speed of the female mosquito such that f' is equal to the frequency of buzz of the male mosquito (6*10^12 Hz). Rearranging the above equation, we have