Waves Ques 46
46. An organ pipe $P_1$ closed at one end vibrating in its first overtone and another pipe $P_2$, open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of $P_1$ and $P_2$ respectively are given by
[1997]
(a) $1: 2$
(b) $1: 3$
(c) $3: 8$
(d) $3: 4$
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Answer:
Correct Answer: 46.(c)
Solution:
- (c) We know that the length of pipe closed at one end for first overtone $(l_1)=\frac{3 \lambda}{4}$
and length of the open pipe for third overtone $(l_2)=\frac{4 \lambda}{2}=2 \lambda$.
Therefore, the ratio of lengths $\frac{l_1}{l_2}=\frac{3 \lambda / 4}{2 \lambda}=\frac{3}{8}$ or $l_1: l_2=3: 8$.
In an open pipe all harmonics are present whereas in a closed organ pipe only alternate harmonies of frequencies are present. Hence musical sound produced by an open organ pipe is sweeter than that produced by a closed organ pipe.
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