First slide

Stationary waves

Question

An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in third harmonic. The ratio of length of two pipes is

Moderate

A

1 : 2
B

4 : 1
C

8 : 3
D

3 : 8

Solution

In first overtone of organ pipe open at one end,
end, $n_{c} = \frac{3 v}{4 l_{c}}$ .....(i)
Third harmonic or second overtone of organ pipe open at both end, $n_{0} = \frac{3 v}{2 l_{0}}$ .....(ii)
given $n_{c} = n_{o} \Rightarrow \frac{3 v}{4 l_{c}} = \frac{3 v_{0}}{2 l_{0}} \Rightarrow \frac{l_{c}}{l_{o}} = \frac{1}{2} .$

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