What Speed Is the Bat Catching Up to Its Prey?

[jrrodri7]

Homework Statement

Assuming the speed of sound is 338 m/s:

A bat moving at 6.2 m/s is chasing a flying insect. The bat emits a 53 KHz chirp and receives an echo at 53.6 KHz. At what speed is the bat catching up on its prey?

Homework Equations

$$f^{'}$$=[ ($$V_{Air}$$ + $$V_{observer}$$) $$/$$ ($$V_{Air}$$ - $$V_{source}$$ ] * f

The Attempt at a Solution

I assumed that since the objects are moving in the same direction I said that the signs are different, but I don't know which one should be positive or negative because normally the signs are the same because Doppler effect usually comes into play when the objects are moving towards or away from each other, but these are moving in the same direction, while the bat is moving quicker and accelerating towards the prey...I just plugged in the numbers, but I don't know which way to work with it...Help?

My answers for Vo (+) and Vs (-) was...Vo = 2.4 m/s
With the Vo (-) and Vs (+) I arrived at...Vo = 10.096

 

[alphysicist]

Hi jrrodri7,

Homework Statement

Assuming the speed of sound is 338 m/s:

A bat moving at 6.2 m/s is chasing a flying insect. The bat emits a 53 KHz chirp and receives an echo at 53.6 KHz. At what speed is the bat catching up on its prey?

Homework Equations

$$f^{'}$$=[ ($$V_{Air}$$ + $$V_{observer}$$) $$/$$ ($$V_{Air}$$ - $$V_{source}$$ ] * f

The Attempt at a Solution

I assumed that since the objects are moving in the same direction I said that the signs are different, but I don't know which one should be positive or negative because normally the signs are the same because Doppler effect usually comes into play when the objects are moving towards or away from each other, but these are moving in the same direction, while the bat is moving quicker and accelerating towards the prey...I just plugged in the numbers, but I don't know which way to work with it...Help?

I don't believe that is correct. If they are both moving towards each other, then the signs in numerator and denominator should be different.

When the observer is moving towards the source, the observed frequency is greater, so in that case the numerator has a positive sign.

When the source is moving towards the observer, the observed frequency is greater, so the denominator has the negative sign.

So in this problem, which would it be?

Also, they are talking about the reflected wave, so you'll need to use the formula twice. What do you get?

My answers for Vo (+) and Vs (-) was...Vo = 2.4 m/s
With the Vo (-) and Vs (+) I arrived at...Vo = 10.096