An open organ pipe of length l is sounded tog | vedclass

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

Question

(C) The fundamental frequency of an open organ pipe of length $l$ is given by $f_1 = \frac{v}{2l}$.The fundamental frequency of an open organ pipe of

Vedclass · Accepted Answer

$\frac{vx}{2l^2}$

Vedclass · Answer

(C) The fundamental frequency of an open organ pipe of length $l$ is given by $f_1 = \frac{v}{2l}$.The fundamental frequency of an open organ pipe of length $(l+x)$ is given by $f_2 = \frac{v}{2(l+x)}$.The beat frequency is the difference between the two frequencies: $f_{beat} = |f_1 - f_2|$.$f_{beat} = \frac{v}{2l} - \frac{v}{2(l+x)} = \frac{v}{2} \left( \frac{1}{l} - \frac{1}{l+x} \right)$.$f_{beat} = \frac{v}{2} \left( \frac{l+x-l}{l(l+x)} \right) = \frac{v}{2} \left( \frac{x}{l(l+x)} \right)$.Since $x Therefore,$f_{beat} \approx \frac{v}{2} \left( \frac{x}{l^2} \right) = \frac{vx}{2l^2}$.

An open organ pipe of length $l$ is sounded together with another organ pipe of length $l + x$ in their fundamental tones $(x << l)$. The beat frequency heard will be (speed of sound is $v$):

Similar Questions

An air column is of length $17 \ cm$. The ratio of frequencies of the $5^{\text{th}}$ overtone for an air column closed at one end to that open at both ends is (velocity of sound in air $= 340 \ ms^{-1}$).

$A$ metal rod of length $125 \ cm$ is clamped at its midpoint. If the speed of sound in the metal is $5000 \ ms^{-1}$, then the fundamental frequency of the longitudinal vibrations of the rod is (in $kHz$)

$A$ closed organ pipe has length $l$. The air in it is vibrating in the $3^{rd}$ overtone with a maximum displacement amplitude $a$. The displacement amplitude at a distance $l/7$ from the closed end of the pipe is:

$A$ standing wave in a pipe with a length $L=1.2 \,m$ is described by $y(x, t)=y_0 \sin [(2 \pi / L) x] \sin [(2 \pi / L) x+\pi / 4]$. Based on the above information,which one of the following statements is incorrect? (Speed of sound in air is $300 \,ms^{-1}$)

In the fundamental mode,the time required for a sound wave to reach the closed end of a pipe filled with air is $t$ seconds. The frequency of vibration of the air column is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module