(B) Given that, the amplitudes of the two waves are $a_1 = a_2 = 10 \,mm$.The phase difference between the waves is $\phi = 90^{\circ}$.The resultant

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(B) Given that, the amplitudes of the two waves are $a_1 = a_2 = 10 \,mm$.The phase difference between the waves is $\phi = 90^{\circ}$.The resultant amplitude $A$ of two interfering waves is given by the formula:$A = \sqrt{a_1^2 + a_2^2 + 2 a_1 a_2 \cos \phi}$Substituting the given values into the formula:$A = \sqrt{(10)^2 + (10)^2 + 2(10)(10) \cos 90^{\circ}}$Since $\cos 90^{\circ} = 0$, the expression simplifies to:$A = \sqrt{100 + 100 + 0}$$A = \sqrt{200}$$A = 10 \sqrt{2} \,mm$

Class 11 Physics Waves and Sound Principle of superposition of waves

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Two identical sinusoidal waves each of amplitude $10 \,mm$, with a phase difference of $90^{\circ}$ are travelling in the same direction in a string. The amplitude of the resultant wave is

AP EAMCET 2021 All AP EAMCET

A
$5 \,mm$
B
$10 \sqrt{2} \,mm$
C
$5 \sqrt{2} \,mm$
D
$20 \,mm$

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Waves and Sound

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Principle of superposition of waves

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The equations of two waves are given by
$y_{1}=5 \sin 2 \pi(x-v t) \, cm$
$y_{2}=3 \sin 2 \pi(x-v t+1.5) \, cm$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........$cm$.

MediumJEE MAIN 2022

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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:

DifficultMHT CET 2023

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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:

Medium

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Give noticeable points about the amplitude of resultant waves of two harmonic progressive waves on a stretched string.

Medium

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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

Easy

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Two identical sinusoidal waves each of amplitude $10 \,mm$, with a phase difference of $90^{\circ}$ are travelling in the same direction in a string. The amplitude of the resultant wave is

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The equations of two waves are given by$y_{1}=5 \sin 2 \pi(x-v t) \, cm$$y_{2}=3 \sin 2 \pi(x-v t+1.5) \, cm$These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........$cm$.

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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The equations of two waves are given by
$y_{1}=5 \sin 2 \pi(x-v t) \, cm$
$y_{2}=3 \sin 2 \pi(x-v t+1.5) \, cm$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........$cm$.