A stationary source generates 5.0 Hz water waves whose speed is 2.0 m/s.A boat is approaching the source at 1.0 m/s.The frequency of these waves, as observed by a person in the boat, is:
A)2.5 Hz
B)5.0 Hz
C)7.5 Hz
D)15 Hz
E)30 Hz

Question

Quizplus · Accepted Answer

The frequency observed by a person in the boat can be calculated using the formula:

f' = (v +/- v_r)/lambda

where f' is the observed frequency, v is the speed of the wave, v_r is the velocity of the observer relative to the source, and lambda is the wavelength.

In this case, the frequency of the wave generated by the source is 5.0 Hz, and the speed of the wave is 2.0 m/s. The boat is approaching the source at 1.0 m/s, so the velocity of the observer relative to the source is -1.0 m/s (negative because the boat is moving towards the source).

The wavelength of the wave can be calculated using the formula:

lambda = v/f

where f is the frequency of the wave.

Substituting the given values, we get:

lambda = 2.0/5.0 = 0.4 m

Substituting these values in the formula for observed frequency, we get:

f' = (2.0 - 1.0)/0.4 = 2.5 Hz (using the minus sign because the observer is approaching the source)

Therefore, the frequency of the waves observed by a person in the boat is 2.5 Hz, which corresponds to choice C.

A Stationary Source Generates 5