Question

Horseshoe bats use the Doppler effect to determine their location. A horseshoe bat flies toward a wall at a speed of 19 m/s while emitting a sound of frequency 37 kHz. What is the beat frequency between the emission frequency and the echo?

Answer 1

`Deltaf=4.09xx10^3"Hz"`

Explanation:

The bat emits a sound which is reflected off the wall. This then interferes with the incoming signal to produce beats.

The incoming signal is "Doppler Shifted" twice because it has been reflected off a wall to which the bat is moving.

To get the beat frequency you find the difference between the two frequencies.

I will assume that at 20 degC the speed of sound `v` is `343.7"m/s"`

The beat frequency between a transmitted signal and a reflected signal off a moving object is:

`f_("reflected")-f_("transmitted")=Deltaf=(2v_("target"))/(v).f`

In relative terms we can consider the wall to be moving towards the bat.

`:.Deltaf=(2xx19)/(343.7)xx37xx10^3`

`Deltaf=4.09xx10^3"Hz"`

Police radar guns measure vehicle speeds like this.