In each of the following two situations a source emits sound with a frequency of 1000 Hz.In situation I the source is moving at 100 m/s toward an observer at rest.In situation II the observer is moving at 100 m/s toward the source, which is stationary.The speed of sound is 340 m/s.The frequencies heard by the observers in the two situations are:
A)I: 1417 Hz; II: 1294 Hz
B)I: 1417 Hz; II: 1417 Hz
C)I: 1294 Hz; II: 1294 Hz
D)I: 773 Hz; II: 706 Hz
E)I: 773 Hz; II: 773 Hz

Question

Quizplus · Accepted Answer

In situation I, the source is moving towards the observer. This means that the frequency of the sound waves will appear higher to the observer. We can use the formula:

$f_{obs}=\left(\frac{v\pm v_{obs}}{v\pm v_s}\right)f_s$

Where $f_s$ is the frequency emitted by the source, $v$ is the speed of sound, $v_s$ is the velocity of the source (positive when moving towards the observer), and $v_{obs}$ is the velocity of the observer (positive when moving towards the source).

Plugging in the values for situation I, we get:

$f_{obs}=\left(\frac{340+100}{340}\right)1000=1417 Hz$

In situation II, the observer is moving towards the source. This means that the frequency of the sound waves will also appear higher to the observer. Plugging in the values for situation II, we get:

$f_{obs}=\left(\frac{340}{340-100}\right)1000=1294 Hz$

Therefore, the answer is choice A) I: 1417 Hz; II: 1294 Hz.

In Each of the Following Two Situations a Source Emits