(B) The resultant amplitude $A$ of two superimposing waves with equal amplitude $a$ is given by the formula: $A^2 = a^2 + a^2 + 2a^2 \cos \phi$,where

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(B) The resultant amplitude $A$ of two superimposing waves with equal amplitude $a$ is given by the formula: $A^2 = a^2 + a^2 + 2a^2 \cos \phi$,where $\phi$ is the phase difference.Given that the resultant amplitude $A$ is equal to the amplitude of the individual waves,$A = a$.Substituting this into the equation: $a^2 = a^2 + a^2 + 2a^2 \cos \phi$.$a^2 = 2a^2 + 2a^2 \cos \phi$.$-a^2 = 2a^2 \cos \phi$.$\cos \phi = -\frac{1}{2}$.Since $\cos(120^\circ) = -\frac{1}{2}$,the phase difference $\phi = \frac{2\pi}{3}$ radians.

Class 11 Physics Waves and Sound Principle of superposition of waves

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Two waves have equations $x_1 = a \sin(\omega t + \phi_1)$ and $x_2 = a \sin(\omega t + \phi_2)$. If the frequency and amplitude of the resultant wave remain equal to those of the superimposing waves,then the phase difference between them is:

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A
$\frac{\pi}{6}$
B
$\frac{2\pi}{3}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{3}$

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Waves and Sound

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Principle of superposition of waves

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Two waves have equations $x_1 = a \sin(\omega t + \phi_1)$ and $x_2 = a \sin(\omega t + \phi_2)$. If the frequency and amplitude of the resultant wave remain equal to those of the superimposing waves,then the phase difference between them is:

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If the phase difference between two waves is $2\pi$ during superposition,then the resultant amplitude is

Obtain the resultant wave of more than two wave functions by representing the superposition principle mathematically.

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 $I$)

The equation of a simple harmonic progressive wave is given by $y = \frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$. The resultant amplitude of the wave is:

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