What is the correct frequency of the reflected ultrasound received by the bat?

[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 of 40.4kHz compared to the textbook answer of frequency = 41kHz. Using any doppler formula rearrangement doesn't lead me to 41kHz, so what have I done wrong?

 

[Orodruin]

What you have computed is the frequency with which the insect is receiving the ultrasound and thus of the reflected sound in the frame of the indect. The bat is still moving toward the insect when it receives the sound.