Question

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9. An experiment uses microphone moving toward a speaker as a way to measure the speed...

9. An experiment uses microphone moving toward a speaker as a way to measure the speed of sound in different media. In air, the frequency heard by the moving microphone is 20% higher than the frequency of the sound when the microphone is at rest. When the gas in the experimental system is replaced by helium, the frequency heard by the moving microphone is now only 6.8% higher than when the microphone is at rest. Based on this information, what is the speed of sound in helium?

Solutions

Expert Solution

According to doppler

where,

is the velocity of waves in the medium

is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction) and

is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction).

Now for air

It is given that the frequency heard is 20% higher than the frequency of the sound. i.e

putting it in the first equation

Now for helium

It is given that the frequency heard is 6.8% higher than the frequency of the sound. i.e

Putting it in the above equation

From equation 1

We know the speed of the sound in air is 343 m/s at room temperature.

So, the speed of sound in helium at room temperature is

genius_generous answered 1 year ago

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