SATHEE: Waves - Result Question 49

Waves - Result Question 49

51. 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) $1 : 3$

(d) $3 : 4$

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Answer:

Correct Answer: 51. (c)

Solution:

and length of the open pipe for third overtone $(l_{2}) = \frac{4 λ}{2} = 2 λ$ .

Therefore, the ratio of lengths $\frac{l_{1}}{l_{2}} = \frac{3 λ / 4}{2 λ} = \frac{3}{8}$ 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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Waves - Result Question 49

51. An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2, open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of P1 and P2 respectively are given by

Answer:

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51. 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