(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 and Sound 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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Waves and Sound

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Longitudinal Stationary Waves (Organ Pipes) and Resonance Tube

An organ pipe closed at one end has a fundamental frequency of $1500 \ Hz$. The maximum number of overtones generated by this pipe which a normal person can hear is:

DifficultAIIMS 2004

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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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For a particular resonance tube,following are four of the six harmonics below $1000 \,Hz$: $300, 600, 750$ and $900 \,Hz$. The two missing harmonics are:

Medium

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On producing waves of frequency $1000 \text{ Hz}$ in a Kundt's tube,the total distance between $6$ successive nodes is $85 \text{ cm}$. The speed of sound in the gas filled in the tube is ..... $m/s$.

Medium

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In a resonance tube,the first and second resonances are obtained at depths $22.7 \,cm$ and $70.2 \,cm$ respectively. The third resonance will be obtained at a depth of: (in $\,cm$)

MediumMHT CET 2023

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An organ pipe closed at one end has a fundamental frequency of $1500 \ Hz$. The maximum number of overtones generated by this pipe which a normal person can hear is:

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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On producing waves of frequency $1000 \text{ Hz}$ in a Kundt's tube,the total distance between $6$ successive nodes is $85 \text{ cm}$. The speed of sound in the gas filled in the tube is ..... $m/s$.

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