1.

In a large room a person receives direct sound waves from a source 120 m away from him. He also receives waves from the same source which reach him, being reflected from the 25m high ceiling at a point halfway between them. For which wavelengths will these two sound waves interfere constructively ?

Answer»

Solution :As shown in figure, for reflection from the ceiling :

Path SCP = SC + CP =2SC [as `ANGLE I =ANGLER, SC = CP`] or path `SCP = 2sqrt(60^2 +25^2) = 130m`
So path difference between interfering WAVES along paths SCP and SP,
`Deltax = 130 - 120 = 10 m`
Now for constructive intergerence at P, `Deltax = nlambda`,
`i.e., 10 = n lambda " or " lambda=10/n` with n =1,2,3,.......
`i.e.,lambda =10m , 5m , (10//3)m` and so on.


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