(B) The given wave equation is $Y = Y_0 \sin(2 \pi n t - \frac{2 \pi x}{\lambda})$.Comparing this with the standard form $Y = Y_0 \sin(\omega t - kx)$

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(B) The given wave equation is $Y = Y_0 \sin(2 \pi n t - \frac{2 \pi x}{\lambda})$.Comparing this with the standard form $Y = Y_0 \sin(\omega t - kx)$,we get angular frequency $\omega = 2 \pi n$.The maximum particle velocity $v_{p, \text{max}} = Y_0 \omega = Y_0 (2 \pi n) = 2 \pi n Y_0$.The wave velocity $v = n \lambda$.According to the problem,the wave velocity is $(1/8)^{\text{th}}$ of the maximum particle velocity:$v = \frac{1}{8} v_{p, \text{max}}$$n \lambda = \frac{1}{8} (2 \pi n Y_0)$$n \lambda = \frac{\pi n Y_0}{4}$$\lambda = \frac{\pi Y_0}{4}$.

Class 11 Physics Waves and Sound Wave Equation and Characteristics of Waves

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$A$ simple harmonic progressive wave is given by $Y = Y_0 \sin 2 \pi (nt - \frac{x}{\lambda})$. If the wave velocity is $(1/8)^{\text{th}}$ of the maximum particle velocity,then the wavelength is

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A
$\frac{\pi Y_0}{2}$
B
$\frac{\pi Y_0}{4}$
C
$\frac{\pi Y_0}{8}$
D
$\frac{\pi Y_0}{16}$

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Waves and Sound

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Wave Equation and Characteristics of Waves

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DifficultJEE MAIN 2026

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$A$ simple harmonic progressive wave is given by $Y = Y_0 \sin 2 \pi (nt - \frac{x}{\lambda})$. If the wave velocity is $(1/8)^{\text{th}}$ of the maximum particle velocity,then the wavelength is

Similar Questions

$A$ simple harmonic progressive wave is represented as $y = 0.03 \sin \pi (2 t - 0.01 x) \ m$. At a given instant of time,the phase difference between two particles $25 \ m$ apart is

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