The Doppler formula for the frequency detected can be written f = f’ (v - vD) /

Question

The Doppler formula for the frequency detected can be written f = f’ (v - vD) / (v - vS), where f’ is the frequency emitted, v is the speed of sound, vD and vs are suitable components of the detector and source velocities. (vD and vs can be of either sign depending on the direction of the motion relative to the S-D axis.) Suppose the source is traveling at 5 m/s away from the detector, the detector is traveling at 7 m/s toward the source, and there is a 3 m/s wind blowing from the source toward the detector. The values that should be substituted into the Doppler shift equation are (in m/s):

a. vD = 10 vs = 2 b. vD = -7 vs = -5 c. vD = -7 vs = 5 d. vD = 4 vs = 2 e. vD = -10 vs = -8

Explanation / Answer

The principle to be used in calculating Doppler frequency shift if there is a wind blowing is:

When the wind blows in direction from source to detector, add the wind speed to the speed of sound.
When the wind blows in direction from the detector towards the source, substract the wind speed from the speed of sound.

Now, the wind speed is blowing in the direction from source towards the detector, we need to add the wind speed (3 m/s) to the speed of sound (u, say). Thus new sound speed = (u + 3)

The doppler effect formula is then:

Apparent frequency = (original frequence) x [((u+3) + 7)/((u+3) + 5)]
= (original frequency) x [(u + 10)/(u+8)]

This is the same as if the source is travelling at 8 m/s away from the observer, and the observer is travelling at 10 m/s towards the source in still air.

Hence VD = 10m/s and VS = 8m/s

Option E is answer

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