Wave Motion 2 Question 17
17. An open pipe is in resonance in 2 nd harmonic with frequency $f _1$. Now one end of the tube is closed and frequency is increased to $f _2$ such that the resonance again occurs in $n$th harmonic. Choose the correct option.
(2005, 2M)
(a) $n=3, f _2=(3 / 4) f _1$
(b) $n=3, f _2=(5 / 4) f _1$
(c) $n=5, f _2=\frac{5}{4} f _1$
(d) $n=5, f _2=\frac{3}{4} f _1$
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Answer:
Correct Answer: 17. (c)
Solution:
$$ \begin{aligned} & f _1=\frac{v}{l} \quad(2 \text { nd harmonic of open pipe }) \\ & f _2=n\left(\frac{v}{4 l}\right)(n \text {th harmonic of closed pipe }) \end{aligned} $$
Here, $n$ is odd and $f _2>f _1$. It is possible when $n=5$ because with $n=5$
$$ f _2=\frac{5}{4}\left(\frac{v}{l}\right)=\frac{5}{4} f _1 $$
