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Q.

1. In a closed organ pipe, standing waves can be formed.
II. In a closed organ pipe (closed at one end), only odd harmonics are present.
III. The harmonics which are present in a pipe, open at both ends are odd harmonics only.
Which of the following statement(s) related to organ pipe is/are correct?

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a

Only I

b

Both II and III

c

Both I and II

d

I, II and III

answer is C.

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Detailed Solution

In a closed organ pipe, two waves travelling in opposite direction superimpose with each other to develop a wave pattern which is standing or stationary.

Possible wavelengths of stationary waves in this type of organ pipe is given as

λn=4L(2n+1) or λn=4L,4L3,4L5,

As frequency, v=vλ   (On putting, n = 0, 1, 2, 3, …)

So, frequencies of nth harmonics can be given as

vn=v4L,3v4L,5v4L,

v1:v2:v3=1:3:5

So, only odd harmonics are present in case of closed organ pipe.
However, in case of open organ pipe,

frequencies of nth harmonics,  vn=nv2L

Thus, even and odd or all the harmonics are present. 

So, Statements I and II are correct but III is incorrect.

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