physics numercial question form SOUND

Question

a toy car blowing its horn is moving with a steady speed of 5 m/s away from a wall.an oberver towards whom the toy car is moving is able to hear 5 beatsper second.if the velocity of sound in air is 340m/s then frequency of horn of the car is close to? OPTIONS A)510Hz B)340Hz C)170Hz D)680Hz

Answer 1

I know it does not matter at this point, but the previous solution will give you an incorrect answer.  That is because, while it accurately includes the Doppler shift of the frequency heard by the observer directly from the source, it neglects to include that the frequency the observer hears echoing off the wall will be Doppler-shifted the other way, as the source is moving away from the wall.  In this case, the frequency heard echoing off the wall is:

 

F_wall = (340/(v+v_s))f = (340/(340+5))f = (340/345)f

 

So the beat frequency expression should actually be:

 

f_beat = (F - F_wall) = ((340/335)f - (340/345)f) = 5 Hz

 

Solving this expression for f will give one of the answers listed exactly.

Answer 2

When a source of sound is moving toward a stationary observer, the apparent frequency F heard by the observer is

F = f V/(V-v_s)  where V = speed of sound, vs = speed of car, and f = frequency of the source.

F = f 340/(340-5) = 340 f/335

 

Beats are formed by the frequency of the reflected waves f , and the apparent frequency.

Beat frequency = F - f = 340f/335 - f = 5

or     f (340/335 - 1) = 5

 

Solve for f.