What is the correct way to calculate the doppler effect in this scenario?

[slaw155]

A bat uses ultrasound at 40kHz to locate a stationary insect. If bat is flying directly towards the insect at speed of 4m/s at what frequency does the bat receive the ultrasound reflections from the insect? Speed of sound = 340m/s.

I went frequency = frequency of source x (velocity of wave+velocity of bat)/(velocity of wave)
So 40 = f x (340+4)/(340).
This however gives me the wrong answer from the textbook answer of frequency = 41kHz.
What have I done wrong?

 

[guitarphysics]

The problem is this: the insect receives the sound from the bat and there is a doppler effect there. Then the insect becomes the source, and the bat receives the sound, and once again we have the doppler effect.
For the first effect, we have a moving source (and stationary observer). The bat, which is the source, moves towards the insect. So, you need to use a different formula to compute the effect; see here- http://hyperphysics.phy-astr.gsu.edu/hbase/sound/dopp.html
After that, you have the observer approaching the stationary source. The insect, which is now the source, is being approached by the bat, now the observer. Here you can use the formula you named above.
Hopefully you can do the algebra stuff, the main problem you had was conceptual I think. It gave me approx 40.95 kHz.