A bat moving at 5.00 m/s, is chasing a flying insect. If thebat emits a 39.90 kH

Question

A bat moving at 5.00 m/s, is chasing a flying insect. If thebat emits a 39.90 kHz chirp and receives back an echo at 40.60 kHz,at what speed is the insect moving toward or away from the bat?Take the speed of sound in air to be v = 340m/s.
(I previously submitted this question but was given anincorrect answer.) A bat moving at 5.00 m/s, is chasing a flying insect. If thebat emits a 39.90 kHz chirp and receives back an echo at 40.60 kHz,at what speed is the insect moving toward or away from the bat?Take the speed of sound in air to be v = 340m/s.
(I previously submitted this question but was given anincorrect answer.)

Explanation / Answer

Let u is the speed of the insect (assume that it is flying away)and f' is the frequency that the insect "hear" f'=f0*(v-u)/(v-5)=f0*(v-u)/335 Let f'' is the frequency that the bat receives f''=f'*(v+5)/(v+u)=f'*345/(v+u)=f0*(345/335)*(340-u)/(340+u) so (340-u)/(340+u)=(f''/f0)*(335/345)˜0,988 solve this u = 340*(1-0,988)/(1+0,988)=6,9(m/s) u is positive so the insect is truly flying away

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