Video: Doppler Shift

Sound waves are produced by person A, who moves at a speed ๐‘ โ‚ toward a second person, person B. Person B is moving toward person A at a speed ๐‘ โ‚‚, where ๐‘ โ‚‚ is less than ๐‘ โ‚. Which person perceives the sound waves produced by person A as having higher frequency?

02:31

Video Transcript

Sound waves are produced by person A, who moves at a speed ๐‘  one toward a second person, person B. Person B is moving toward person A at a speed ๐‘  two, where ๐‘  two is less than ๐‘  one. Which person perceives the sound waves produced by person A as having higher frequency?

Okay, letโ€™s say that this here is person A and this over here is person B. Weโ€™re told that person A is producing sound waves. And we can model these waves as concentric circles where each circle represents a wavefront of the sound wave. So these wavefronts are moving out in all directions from the source, person A, and theyโ€™re moving at the speed of sound, which is typically around 340 meters per second. Now, not only are the sound waves in motion, but so are person A and person B. Person A is moving at a speed called ๐‘  one toward person B while person B moves toward person A at a different speed, ๐‘  two, which is less than ๐‘  one.

The question is, which of these two people perceives the sound waves produced by person A as having higher frequency? Now, because person A is the source of these sound waves, the frequency perceived by person A is simply the frequency of the waves at their source. That frequency is equal to the number of wavefronts emitted by the source every second. We could say that person A always experiences the same frequency because person A is the source of the sound waves. On the other hand, person B, who is in motion relative to these sound waves, experiences something different. As the sound waves move out from the source and reach person B, the frequency perceived by person B will again depend on the number of wavefronts that pass by person B every second.

If person B and person A were stationary relative to one another, then this number of wavefronts passing by every second would be the same as the number emitted by the source every second. In other words, person B would perceive the same frequency as person A. But we knew that these two people arenโ€™t stationary relative to one another. Person A is moving toward person B and person B moves toward person A.

This means that the number of wavefronts person B passes through every second of time will be greater than they would be if person B was stationary relative to person A. And since the count of wavefronts per second is higher, that means the perceived frequency will be higher as well. So because person B is overall moving toward the source of the sound waves, person A, person B will perceive a higher frequency. And thatโ€™s the answer to our question. Person B perceives the sound waves produced by person A as having higher frequency. And thatโ€™s because there are more wavefronts per second passing by person B than by person A.

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