A siren emitting a sound of frequency 1003 Hz moves away from you toward the face of a cliff at a speed of 12.0 m/s. Take the speed of sound in air as 334 m/s. (a) What is the frequency of the sound you hear coming directly from the siren

(a) Approximately 968 Hz.

Explanation:

The observed frequency is less than 1003 Hz because of Doppler's Effect. When the source is moving away from an observer that doesn't move, the equation for the observed frequency would be:

,

where in the context of this problem,

Apply this equation to find :

.

Here's an alternative explanation.

The frequency of the siren at the source is . That corresponds to a period of .

In other words, at the source, a peak arrives about every .

The source is moving away from the observer at a speed of . In the between the first and the second peak, the source moved away from the observer. It would take an extra for the sound to cover that extra distance.

As a result, the period of the sound would appear to be to the observer.

That corresponds to an observed frequency of . (Same as the answer from the formula.)

newton's first law of motion