In a large room, a person receives direct sound waves froma source 120 metres away from him. He also receives waves from the same source which reach him, being reflected from the 25 metre high ceiling at a point halfway between them. The two waves interfere constuctively for wavelength of

Options

A. `20, 20//3,20//5` etc
B. `10,5, 0//3, 2.5`
C. `10,20,30` etc
D. `15, 25,35` etc

Answer

B

Explanation

Let S be source of sound and P the person or listner.
The waves from S reach point P directly following the patth SMP and being reflected from the ceiling at Point A following the Path SAP. M is mid point of SP(i.e. SM = MP) and `angle = 90^(@)`
Path difference between waves reaching P is
`Deltax = SAP - SMP`
`SAP = SA + AP = 2(SA)`

`SAP = 2sqrt([(SM)^(2) + (MA)^(2)] } = 2sqrt((60^(2) + 25^(2)))` = 130 m
implies Path difference = SAP - SMP = 130 - 120 = 10m
For constructive interference
`Delta x = 10 nlambda`
implies Wavelength `lambda = (10)/(n)`
The possibe wavelength are `lambda = 10, 5, (10)/(3) , 2.5 ...`