in a large room a person receives direct sound wave from a source 120m away from him. He also receive wave from same source which reaches him after being reflected from 25m high ceiling at a point midway between them . two waves interfere constructively for wavelength of (in meter)
Answers
Answer:
20, 20/3, 20/5 etc
Explanation:
Let
S
be source of sound and Pthe person or listner. The waves from
S
reach point Pdirectly following the path SMPand being reflected from the ceiling at point
A
following the path SAP.
M
is mid-point ofSP(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=10m 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
,
?..
=
20
m
,6.67m,4m,2.85m,2.22
m,
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