(D) The resultant amplitude $A_R$ of two waves with amplitudes $A_1$ and $A_2$ and phase difference $\phi$ is given by $A_R = \sqrt{A_1^2 + A_2^2 + 2

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(D) The resultant amplitude $A_R$ of two waves with amplitudes $A_1$ and $A_2$ and phase difference $\phi$ is given by $A_R = \sqrt{A_1^2 + A_2^2 + 2 A_1 A_2 \cos \phi}$.Given $A_1 = A_2 = A$ and $\phi = \pi / 2$.Substituting these values: $A_R = \sqrt{A^2 + A^2 + 2 A^2 \cos(\pi / 2)}$.Since $\cos(\pi / 2) = 0$,we get $A_R = \sqrt{2 A^2} = \sqrt{2} A$.The frequency of the resultant wave remains the same as the frequency of the individual waves,which is $\omega$.

Class 11 Physics Waves and Sound Principle of superposition of waves

Medium

When two sound waves with a phase difference of $\pi / 2$,and each having amplitude $A$ and frequency $\omega$,are superimposed on each other,then the maximum amplitude and frequency of the resultant wave is:

A
$A / \sqrt{2}, \omega / 2$
B
$A / \sqrt{2}, \omega$
C
$\sqrt{2} A, \omega / 2$
D
$\sqrt{2} A, \omega$

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Waves and Sound

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Principle of superposition of waves

Two waves each of intensity $I$ interfere with a phase difference of $120^o$. The resultant intensity of the waves will be:

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Two waves of amplitudes $A_1$ and $A_2$ respectively are superimposed. The ratio between the maximum and minimum intensities of the resultant waves is $9 : 4$. The value of $A_2 / A_1$ is [Assume $A_1 > A_2$]

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$A$ sound wave of wavelength $32 \ cm$ enters the tube at $S$ as shown in the figure. Then the smallest radius $r$ so that a minimum of sound is heard at detector $D$ is ... $cm$.

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If two waves having amplitudes $2A$ and $A$ and same frequency and velocity,propagate in the same direction in the same phase,the resulting amplitude will be

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Two identical waves $1$ and $2$,each of intensity $I_0$,are superimposed. The resulting intensity is:

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When two sound waves with a phase difference of $\pi / 2$,and each having amplitude $A$ and frequency $\omega$,are superimposed on each other,then the maximum amplitude and frequency of the resultant wave is:

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Two waves each of intensity $I$ interfere with a phase difference of $120^o$. The resultant intensity of the waves will be:

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