Statement-1: Two longitudinal waves given by | vedclass

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(C) The intensity $I$ of a wave is given by the formula $I = 2\pi^2 f^2 A^2 \rho v$,where $f$ is frequency,$A$ is amplitude,$\rho$ is density,and $v$

Vedclass · Accepted Answer

Statement-$1$ is True,Statement-$2$ is False.

Vedclass · Answer

(C) The intensity $I$ of a wave is given by the formula $I = 2\pi^2 f^2 A^2 \rho v$,where $f$ is frequency,$A$ is amplitude,$\rho$ is density,and $v$ is wave speed.For wave $1$: $A_1 = 2a$ and $\omega_1 = \omega$ (so $f_1 = \omega / 2\pi$).Intensity $I_1 \propto f_1^2 A_1^2 = (\omega/2\pi)^2 (2a)^2 = 4 \cdot (\omega/2\pi)^2 a^2$.For wave $2$: $A_2 = a$ and $\omega_2 = 2\omega$ (so $f_2 = 2\omega / 2\pi$).Intensity $I_2 \propto f_2^2 A_2^2 = (2\omega/2\pi)^2 (a)^2 = 4 \cdot (\omega/2\pi)^2 a^2$.Since $I_1 = I_2$,Statement-$1$ is True.Statement-$2$ is False because intensity is proportional to the square of both amplitude $AND$ frequency $(I \propto A^2 f^2)$. Therefore,Statement-$1$ is True and Statement-$2$ is False.

Statement-$1$: Two longitudinal waves given by equations $y_1(x, t) = 2a \sin(\omega t - kx)$ and $y_2(x, t) = a \sin(2\omega t - 2kx)$ will have equal intensity.
Statement-$2$: Intensity of waves of given frequency in the same medium is proportional to the square of amplitude only.

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Statement-$1$: Two longitudinal waves given by equations $y_1(x, t) = 2a \sin(\omega t - kx)$ and $y_2(x, t) = a \sin(2\omega t - 2kx)$ will have equal intensity.Statement-$2$: Intensity of waves of given frequency in the same medium is proportional to the square of amplitude only.