(C) For a string of length $l$ fixed at both ends,the boundary conditions require nodes at both ends.This means the length $l$ must be an integer mult

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(C) For a string of length $l$ fixed at both ends,the boundary conditions require nodes at both ends.This means the length $l$ must be an integer multiple of half-wavelengths: $l = n \frac{\lambda}{2}$,where $n = 1, 2, 3, \dots$ is the number of loops or the harmonic number.Rearranging this equation for the wavelength $\lambda$,we get:$\lambda = \frac{2l}{n}$.

Class 11 Physics Waves and Sound Stationary Waves (Standing wave)

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$A$ stretched string of length $l,$ fixed at both ends,can sustain stationary waves of wavelength $\lambda,$ given by:

A
$\lambda = \frac{n^2}{2l}$
B
$\lambda = \frac{l^2}{2n}$
C
$\lambda = \frac{2l}{n}$
D
$\lambda = 2ln$

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Waves and Sound

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Stationary Waves (Standing wave)

Write the equation of a stationary wave and obtain the equations of nodes and antinodes by defining them.

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$A$ wave is represented by the equation $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$. The maximum amplitude and loop length are respectively:

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Standing waves are produced in a $10 \, m$ long stretched string fixed at both ends. If the string vibrates in $5$ segments and the wave velocity is $20 \, m/s$,the frequency is ....... $Hz$.

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$A$ string vibrates according to the equation $y = 5 \sin \left( \frac{2\pi x}{3} \right) \cos (20\pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in $sec$. The distance between two adjacent nodes is .... $cm$.

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The figure shows an incident pulse $P$ reflected from a rigid support. Which one of $A, B, C, D$ represents the reflected pulse correctly?

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$A$ stretched string of length $l,$ fixed at both ends,can sustain stationary waves of wavelength $\lambda,$ given by:

Similar Questions

Write the equation of a stationary wave and obtain the equations of nodes and antinodes by defining them.

$A$ wave is represented by the equation $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$. The maximum amplitude and loop length are respectively:

Standing waves are produced in a $10 \, m$ long stretched string fixed at both ends. If the string vibrates in $5$ segments and the wave velocity is $20 \, m/s$,the frequency is ....... $Hz$.

$A$ string vibrates according to the equation $y = 5 \sin \left( \frac{2\pi x}{3} \right) \cos (20\pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in $sec$. The distance between two adjacent nodes is .... $cm$.

The figure shows an incident pulse $P$ reflected from a rigid support. Which one of $A, B, C, D$ represents the reflected pulse correctly?

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