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Waves y(1) = Acos(0.5pix - 100pit) and y...

Waves `y_(1) = Acos(0.5pix - 100pit)` and `y_(2)=Acos(0.46pix - 92pit)` are travelling along x-axis. (Here `x` is in `m` and `t` is in second)
(2) The wave velocity of louder sound is

A

The number of times intensity is maximum in time interval of 1 second is 4

B

The wave velocity of louder sound is 200 m/s

C

The number of times `y_(1)+y_(2)=0` at `x=0` in 1 sec is 100

D

The time gap between two consecutive loud sounds (beat period) is 0.25 seconds

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`y_(1)=Acos(0.5pix-100pit)and y_(2)=Acos(0.46pix-92pit)`
For small difference in frequency beats will be produced.
`2pif_(1)=100pi implies f_(1)=50 and 2pif_(2) =92pi implies f_(2)=46`
Beat frequency `=|f_(1)-f_(2)|=4`
`V=(w)/(k)=(100pi)/(0.5pi)=(92pi)/(0.46)=200m//s` (same since it depends on medium)
`y_(1)+y_(2)=0` [at x=0]
`implies cos 100pit+cos92pit=0 implies cos96pitxxcos4pit=0`
It can be zero 100 times in 1 second.
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