How Fast is the Insect Moving Towards the Bat in a Doppler Effect Scenario?

[Daniiel]

A bat is chasing an insect. if the bat, moving at 6m/s emits a 40kHz sound and receives back an echo at 40.4 kHz. What speed and direction is the insect moving? take the speed of sound to be 343m/sOkay sooo.
ive mucked around with this a fair bit

so i know before f'>f that, so the insect is moving towards the bat

f' = f( (v + Vd) / (v- Vs) )
so the bat is both the source and detector
i tried to write it in terms of the insect
so Vd = Vb - Vi
and Vs = Vb - Vi

so i get Vi = f( V + Vb) + f' ( -v + Vb) all over f + f '
which = 4.29 m/s
is that correct?

 

[anathema]

Yes, your calculation is correct. The speed of the insect is 4.29 m/s towards the bat. This is because the received frequency (f') is higher than the emitted frequency (f), indicating that the insect is moving towards the bat. By using the formula for the Doppler effect and substituting the values given, you were able to calculate the insect's speed accurately. Great job!