Wave Motion 2 Question 21
21. An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by $100 Hz$ then the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is
(1996, 2M)
(a) $200 Hz$
(b) $300 Hz$
(c) $240 Hz$
(d) $480 Hz$
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Answer:
Correct Answer: 21. (a)
Solution:
- Length of the organ pipe is same in both the cases.
Fundamental frequency of open pipe is $f _1=\frac{v}{2 l}$ and
Frequency of third harmonic of closed pipe will be
$$ f _2=3\left(\frac{v}{4 l}\right) $$
Given that,
$$ f _2=f _1+100 $$
or $f _2-f _1=100$ or $\frac{3}{4}\left(\frac{v}{l}\right)-\left(\frac{1}{2}\right)\left(\frac{v}{l}\right)=100$
$\Rightarrow \frac{v}{4 l}=100 Hz \quad \therefore \quad \frac{v}{2 l} \quad$ or $\quad f _1=200 Hz$
Therefore, fundamental frequency of the open pipe is $200 Hz$.
