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A source when at rest in a medium produces waves to the right with a velocity v and a...

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saj-94 | Salutatorian

Posted September 1, 2013 at 1:27 PM via web

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A source when at rest in a medium produces waves to the right with a velocity v and a wavelength of λ . If the source is set in motion to the left with a velocity Vs  ( Vs<v ), what would be the magnitude of the wavelengths produced directly in front of the source?

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llltkl | College Teacher | Valedictorian

Posted September 1, 2013 at 4:05 PM (Answer #1)

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When a sound source is moving toward you the sound waves in front of you bunch up, creating a higher frequency sound wave than what the source produces. When it moves away from you, the sound waves behind the source stretch out, creating a lower frequency sound wave than what the source produces. This is known as Doppler effect.

When a sound source, S produces a frequency of n per second, an observer at O and if the speed of sound in the medium is taken as v, and further, if the distance SO is put equal to v, then there will be n complete waves present in the distance SO (plz. see the attached image, here n=6). The wavelength of soundwaves reaching observer would be given by:

`lambda=v/n`

Now, if the source is moving with a speed `v_s (v_sltv)` away from the observer, in one second it produces n waves while it moves through a distance of `v_s` . Thus these n waves will be stretched in a total distance of `(v+v_s)` .

The new wavelength of soundwaves reaching the observer would be:

`lambda'=(v+v_s)/n`

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