In a large room, a person receives direct sound waves from a source 120 metres away from him. He also receive waves from the same source which reach, being reflected from the 25 metres high ceiling, at a point halfway between them. The two waves interfere constructively for a wavelength of
Answers
Let S
be source of sound and
P
the person or listner. The waves from
S reach point P directly following the path 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
∠SMA=
90
o
Path difference between waves
Δx=SAP−SMP
We have
SAP=SA+AP=2(SA)
=
2
[
(SM)
2
+
(MA)
2
]
−−−−−−−−−−−−−−
√
=
2
(
60
2
+
25
2
)
−−−−−−−−−
√
=130 m∴
Path difference = SAP ? SMP
=130−120=10
m Path difference due to reflection from ceiling =
λ
2
∴
Effective path difference Dx =
10+
λ
2
For constructive interference
Δx=10+
λ
2
=nλ⇒(2n−1)
λ
2
=10(n=1,2,3....)∴ Wavelength
λ=
2×10
(2n−1)
=
20
2n−1
. The possible wavelength are l
=
20,
20
3
,
20
5
,
20
7
,
20
9