(A) The fundamental frequency $(n_0)$ of a string of length $d$ fixed at both ends is given by the formula: $n_0 = \frac{1}{2d} \sqrt{\frac{T}{\mu}}$.

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(A) The fundamental frequency $(n_0)$ of a string of length $d$ fixed at both ends is given by the formula: $n_0 = \frac{1}{2d} \sqrt{\frac{T}{\mu}}$.Since the cord vibrates in its simplest standing-wave state (fundamental mode),the frequency of vibration $f$ is equal to the fundamental frequency $n_0$.Therefore,$f = \frac{1}{2d} \sqrt{\frac{T}{\mu}}$.Squaring both sides,we get: $f^2 = \frac{1}{4d^2} \cdot \frac{T}{\mu}$.Rearranging to solve for tension $T$: $T = 4\mu f^2 d^2$.

Class 11 Physics Waves Longitudinal Stationary Waves (Organ Pipes) and Resonance Tube

Medium

One insulated conductor from a household extension cord has a mass per unit length of $\mu$. $A$ section of this conductor is held under tension between two clamps. $A$ subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the length of the cord. When the cord carries an $AC$ current of $i$ at a frequency of $f$,it vibrates in resonance in its simplest standing-wave vibration state. Determine the relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.

A
$T=4\mu f^2d^2$
B
$T=2\mu f^2d^2$
C
$T=\frac{\mu f^2d^2}{2}$
D
$T=\frac{\mu f^2d^2}{4}$

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Longitudinal Stationary Waves (Organ Pipes) and Resonance Tube

$A$ pipe of $30 \text{ cm}$ long and open at both ends produces harmonics. Which harmonic mode of the pipe resonates with a $1.1 \text{ kHz}$ source? (Given: speed of sound in air $v = 330 \text{ ms}^{-1}$)

EasyKCET 2014

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When an open pipe is closed from one end, the second overtone of the closed pipe is higher in frequency by $100 \text{ Hz}$ than the first overtone of the open pipe. The fundamental frequency of the open pipe will be (Neglect end correction). (in $\text{ Hz}$)

DifficultMHT CET 2026

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The harmonics which are present in a pipe open at one end are

Easy

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$A$ closed organ pipe and an open organ pipe of the same length produce $2$ beats per second when they are set into vibrations together in their fundamental mode. The length of the open pipe is now halved and that of the closed pipe is doubled. The number of beats produced per second will be:

DifficultAP EAMCET 2020

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The fundamental frequency of a closed pipe is $220 \ Hz$. If $\frac{1}{4}$ of the pipe is filled with water,the frequency of the first overtone of the pipe now is ..... $Hz$.

Medium

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$A$ pipe of $30 \text{ cm}$ long and open at both ends produces harmonics. Which harmonic mode of the pipe resonates with a $1.1 \text{ kHz}$ source? (Given: speed of sound in air $v = 330 \text{ ms}^{-1}$)

When an open pipe is closed from one end, the second overtone of the closed pipe is higher in frequency by $100 \text{ Hz}$ than the first overtone of the open pipe. The fundamental frequency of the open pipe will be (Neglect end correction). (in $\text{ Hz}$)

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