How Far Must a Sound Source Move to Create Silence Due to the Doppler Effect?

[beastysk8er]

Homework Statement

Two adjacent sources each emit frequency 800 hz in air (340 m/s). how far would source 1 have to be moved so an observer in front of the sources would hear no sound? .321 .213 .123 or .312.

Homework Equations

f' = f/(1+ vsource/vsnd)

The Attempt at a Solution

i tried to calculate wavelength so that the frequency is below 20 hz (human limit) and figure it out from there but I am stuck? please help, thank you

 

[Gear300]

The observer wasn't specified to be human...so we cannot assume that we would have to take it so that the frequency is below 20Hz. Rather, what you should do is find the distance of separation between the 2 sources so that the waves they emit destructively interfere (the waves are out of phase by pi).

 

[thomate1]

The Doppler effect is a phenomenon in which the perceived frequency of a sound wave changes when the source of the sound is in motion relative to the observer. This change in frequency is caused by the compression or stretching of the sound waves as the source moves towards or away from the observer.

In this scenario, we have two adjacent sources emitting sound at a frequency of 800 Hz. The speed of sound in air is 340 m/s. To determine the distance that source 1 would have to be moved for an observer in front of the sources to hear no sound, we can use the equation for the Doppler effect:

f' = f/(1+ vsource/vsnd)

Where:
f' is the perceived frequency
f is the actual frequency
vsource is the velocity of the source
vsnd is the velocity of sound

In this case, we want the perceived frequency to be 0 Hz (no sound). We know the actual frequency (800 Hz) and the velocity of sound (340 m/s). Therefore, we can rearrange the equation to solve for the velocity of the source:

vsource = -f * vsnd / (f' - f)

Plugging in the values, we get:
vsource = -800 Hz * 340 m/s / (0 Hz - 800 Hz)
vsource = 272 m/s

This means that source 1 would have to move away from the observer at a velocity of 272 m/s in order for the observer to hear no sound. The distance that source 1 would have to move can be calculated using the equation for velocity:

v = d/t

Where:
v is the velocity
d is the distance
t is the time

In this case, we know the velocity (272 m/s) and can assume a reasonable time (such as 1 second). Therefore, the distance that source 1 would have to move is approximately 272 meters.

In conclusion, for an observer in front of the sources to hear no sound, source 1 would have to be moved away from the observer at a velocity of 272 m/s for a distance of 272 meters.