The lengths of the two pipes open at both end | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a pipe open at both ends, the fundamental frequency is given by $f = \frac{v}{2l}$, where $v$ is the velocity of sound and $l$ is the length o

Vedclass · Accepted Answer

$\frac{vL_1}{2L(L + L_1)}$

Vedclass · Answer

(C) For a pipe open at both ends, the fundamental frequency is given by $f = \frac{v}{2l}$, where $v$ is the velocity of sound and $l$ is the length of the pipe.For the first pipe of length $L$, the frequency is $f_1 = \frac{v}{2L}$.For the second pipe of length $(L + L_1)$, the frequency is $f_2 = \frac{v}{2(L + L_1)}$.The beat frequency is the difference between the two frequencies: $f_b = |f_1 - f_2|$.$f_b = \left| \frac{v}{2L} - \frac{v}{2(L + L_1)} \right| = \frac{v}{2} \left| \frac{(L + L_1) - L}{L(L + L_1)} \right|$.$f_b = \frac{v}{2} \left( \frac{L_1}{L(L + L_1)} \right) = \frac{vL_1}{2L(L + L_1)}$.

The lengths of the two pipes open at both ends are $L$ and $(L + L_1)$. If they are sounded together, the beat frequency will be ($v$ = velocity of sound in air)

Similar Questions

Three sound waves of equal amplitudes have frequencies $(n - 1)$,$n$,and $(n + 1)$. They superimpose to produce beats. The number of beats produced per second is:

Two waves $Y_1 = 0.25 \sin(316t)$ and $Y_2 = 0.25 \sin(310t)$ are propagating along the same direction. The number of beats produced per second is:

Two identical wires have the same fundamental frequency of $400 \text{ Hz}$ when kept under the same tension. If the tension in one wire is increased by $2\%$,the number of beats produced will be

When two waves of almost equal frequencies $v_1$ and $v_2$ reach a point simultaneously,the time interval between successive maxima is

Two sound waves travelling in the same direction have displacements $y_1 = a \sin(0.2 \pi x - 50 \pi t)$ and $y_2 = a \sin(0.15 \pi x - 46 \pi t)$. How many times can a listener hear sound of maximum intensity in one second?

Vedclass Test Series

Exam Paper Generator

Online Exam Module