I NEED HELP PLEASE! :) A train is moving at 23 m/s due east when it sounds a blast on its horn, frequency = 164 Hz. What frequency is heard by the driver of a car moving due east at 15 m/s along a road parallel to the tracks? Use 343 m/s for the speed of sound. Please show all work.

168 Hz

Explanation:

The Doppler equation describes how sound frequency depends on relative velocities:

fr = fs (c + vr) / (c + vs),

where fr is the frequency heard by the receiver,

fs is the frequency emitted at the source,

c is the speed of sound,

vr is the velocity of the receiver,

and vs is the velocity of the source.

Note: vr is positive if the receiver is moving towards the source, negative if away.

Conversely, vs is positive if the receiver is moving away from the source, and negative if towards.

Given:

fs = 164 Hz

c = 343 m/s

vr = -15 m/s

vs = -23 m/s

fr = fs (c + vr) / (c + vs)

fr = 164 Hz (343 m/s − 15 m/s) / (343 m/s − 23 m/s)

fr = 168 Hz

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