How fast in kilometers per hour, must a sound source be moving toward you to make the observed frequency 5.0% greater than that observed when the source is stationary with respect to you? (Assume that the speed of sound is 340 m/s.)
How fast in kilometers per hour, must a sound source be moving toward you to make the observed frequency 5.0% greater than that observed when the source is stationary with respect to you? (Assume that the speed of sound is 340 m/s.)
(You know, you would think with 2 and 1/2 degrees in Physics under my belt I'd have the Doppler equations memorized, wouldn't you? )Originally Posted by Celia
For a source moving toward an object
$\displaystyle f' = f \left ( \frac{v + v_0}{v} \right ) $
where f' is the observed frequency, f is the frequency of the source measured when it isn't moving, v is the speed of sound, and v0 is the speed that the observer is moving toward the source. (We are taking the source to be stationary.)
According to the problem statement f' is 5% larger than f, so f' = 1.05f. Thus:
$\displaystyle 1.05f = f \left ( \frac{340 + v_0}{340} \right ) $
The f's cancel and you can solve for v0. NOTE: Your answer will be in m/s, so you have to convert to km/h from here.
-Dan