Wave Motion Ques 31
- 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: 31.(a)
Solution:
Formula:
- 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 $200 Hz$.
BETA
