(C) The resultant amplitude $A$ of two interfering waves with amplitudes $a_1$ and $a_2$ and phase difference $\phi$ is given by the formula:$A = \sqr

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(C) The resultant amplitude $A$ of two interfering waves with amplitudes $a_1$ and $a_2$ and phase difference $\phi$ is given by the formula:$A = \sqrt{a_1^2 + a_2^2 + 2a_1a_2 \cos \phi}$Given values are $a_1 = 0.3 \ cm$,$a_2 = 0.4 \ cm$,and $\phi = \pi/2$.Substituting these values into the formula:$A = \sqrt{(0.3)^2 + (0.4)^2 + 2(0.3)(0.4) \cos(\pi/2)}$Since $\cos(\pi/2) = 0$,the expression simplifies to:$A = \sqrt{0.09 + 0.16 + 0} = \sqrt{0.25} = 0.5 \ cm$.

Class 11 Physics Waves and Sound Principle of superposition of waves

Medium

Two sound waves (expressed in $CGS$ units) given by $y_1 = 0.3 \sin \frac{2\pi}{\lambda}(vt - x)$ and $y_2 = 0.4 \sin \frac{2\pi}{\lambda}(vt - x + \theta)$ interfere. The resultant amplitude at a place where phase difference is $\pi/2$ will be .... $cm$.

A
$0.7$
B
$0.1$
C
$0.5$
D
$\frac{1}{10}\sqrt{7}$

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Waves and Sound

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Principle of superposition of waves

The amplitude of a wave,represented by the displacement equation $y = \frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$,will be:

MediumAP EAMCET 2023

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Medium

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Three harmonic waves having equal frequency $v$ and same intensity $I_{0}$,have phase angles $0, \frac{\pi}{4}$ and $-\frac{\pi}{4}$ respectively. When they are superimposed,the intensity of the resultant wave is close to

MediumJEE MAIN 2020

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If two waves represented by $y_1 = 4\sin \omega t$ and $y_2 = 3\sin (\omega t + \pi/3)$ interfere at a point,the amplitude of the resulting wave will be about

Medium

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Two sound waves having intensities $I$ and $4I$ interfere to produce an interference pattern. The phase difference between the waves is $\pi / 2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is (in $I$)

Difficult

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Two sound waves (expressed in $CGS$ units) given by $y_1 = 0.3 \sin \frac{2\pi}{\lambda}(vt - x)$ and $y_2 = 0.4 \sin \frac{2\pi}{\lambda}(vt - x + \theta)$ interfere. The resultant amplitude at a place where phase difference is $\pi/2$ will be .... $cm$.

Similar Questions

The amplitude of a wave,represented by the displacement equation $y = \frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$,will be:

The equations of motion for two waves traveling in the same direction are given by ${y_1} = A\sin (\omega t - kx)$ and ${y_2} = A\sin (\omega t - kx - \theta )$. The resultant amplitude of the medium particle will be

Three harmonic waves having equal frequency $v$ and same intensity $I_{0}$,have phase angles $0, \frac{\pi}{4}$ and $-\frac{\pi}{4}$ respectively. When they are superimposed,the intensity of the resultant wave is close to

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