The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce 3 beats. The length of open pipe is made ( 3 1 ) r d and closed pipe is made 3 ti

Question

The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce 3 beats. The length of open pipe is made ( 3 1 ​ ) r d and closed pipe is made 3 times the original, the number of beats produced will be {neglect end correction}

TestHub · Accepted Answer

Let the original length of both pipes be $L$ and the speed of sound be $v$ .

The frequency of the first overtone of the open pipe is $f_{o 1} = \frac{2 v}{2 L} = \frac{v}{L}$ .

The frequency of the first overtone of the closed pipe is $f_{c 1} = \frac{3 v}{4 L}$ .

Given that they produce $3$ beats per second:

$f_{o 1} - f_{c 1} = 3$

$\frac{v}{L} - \frac{3 v}{4 L} = 3$

$\frac{v}{4 L} = 3 \Rightarrow \frac{v}{L} = 12$

When the length of the open pipe is made $\frac{L}{3}$ , its new fundamental frequency is:

$f_{o}^{'} = \frac{v}{2 ( \frac{L}{3} )} = \frac{3 v}{2 L} = \frac{3}{2} \times 12 = 18$

When the length of the closed pipe is made $3 L$ , its new fundamental frequency is:

$f_{c}^{'} = \frac{v}{4 ( 3 L )} = \frac{v}{12 L} = \frac{1}{12} \times 12 = 1$

The new number of beats produced is:

$f_{o}^{'} - f_{c}^{'} = 18 - 1 = 17$

Answer: $17$

Physics - Sound Wave Question with Solution | TestHub

Options:

Doubts & Discussion