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Two tuning forks produce 4 beats per sec...

Two tuning forks produce `4` beats per seconds when they are sounded together. Now both the forks are moved towards the observer at same speed `(u)`. The beat frequency now becomes `5 Hz`. If the observer also beings to run with speed `u` towards both the forks, then beat frequency is.

A

`2 Hz`

B

`4 Hz`

C

`6 Hz`

D

`8 Hz`

Text Solution

Verified by Experts

The correct Answer is:
C
The frequencies of two forks are assumed to be `f` and `f + 4` When forks are moving towards the observer, the frequencies received by the observer are
`f_(1) = f((v)/(v- u))` and `f_(2) = (f + 4)((v)/(v-u))`
`:. Deltaf = f_(2) - f_(1) = 4((v)/(v-u))`
`:. 5 = 4 ((v)/(v-u))`
`rArr 5v - 5u = 4v , rArr u = (v)/(5)`
when observer also begins to run, the frequencies received by him will be
`f'_(1) = f((v + u)/(v - u))` and `f'_(2) = (f + 4)((v + u)/(v - u))`
`:. Deltaf = f'_(2) - f'_(1) = 4 ((v + u)/(v-u))`
`= 4 ((v + (v)/(5))/(v - (v)/(5))) = 4,(6)/(4) = 6 Hz`
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