(B) Let the amplitude of each wave be $a$. The resultant amplitude $A$ is given by the formula:$A^2 = a_1^2 + a_2^2 + 2a_1a_2 \cos \phi$Given $a_1 = a

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(B) Let the amplitude of each wave be $a$. The resultant amplitude $A$ is given by the formula:$A^2 = a_1^2 + a_2^2 + 2a_1a_2 \cos \phi$Given $a_1 = a_2 = a$ and the resultant amplitude $A = a$,we substitute these values:$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 = -1/2$Since $\cos \phi = -1/2$,the phase difference $\phi$ is $2\pi / 3$ radians.

Class 11 Physics Waves and Sound Principle of superposition of waves

Easy

If two waves of the same frequency and same amplitude,on superimposition,produce a resultant disturbance of the same amplitude,the phase difference between the waves is

A
$A) \pi$
B
$B) 2\pi / 3$
C
$C) \pi / 2$
D
$D) 0$

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Class 11 Questions

Class 11

Physics Questions

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Waves and Sound

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Principle of superposition of waves

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

Medium

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The amplitude of the wave resulting from the superposition of $3$ waves given by $x_1 = A \cos \omega t$,$x_2 = 2 A \sin \omega t$ and $x_3 = \sqrt{2} A \cos (\omega t + \frac{\pi}{4})$ is

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When two waves of the same amplitude $a$ and the same frequency $f$ superimpose,the total intensity is proportional to which of the following?

Easy

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Two waves originating from $S_1$ and $S_2$,having zero initial phase difference and common wavelength $\lambda$,will show completely destructive interference at $P$,if $(S_1 P - S_2 P)$ is

Easy

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Two sound waves of intensity $2 \, W/m^2$ and $3 \, W/m^2$ meet at a point to produce a resultant intensity $5 \, W/m^2$. The phase difference between the two waves is ......

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If two waves of the same frequency and same amplitude,on superimposition,produce a resultant disturbance of the same amplitude,the phase difference between the waves is

Similar Questions

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

The amplitude of the wave resulting from the superposition of $3$ waves given by $x_1 = A \cos \omega t$,$x_2 = 2 A \sin \omega t$ and $x_3 = \sqrt{2} A \cos (\omega t + \frac{\pi}{4})$ is

When two waves of the same amplitude $a$ and the same frequency $f$ superimpose,the total intensity is proportional to which of the following?

Two waves originating from $S_1$ and $S_2$,having zero initial phase difference and common wavelength $\lambda$,will show completely destructive interference at $P$,if $(S_1 P - S_2 P)$ is

Two sound waves of intensity $2 \, W/m^2$ and $3 \, W/m^2$ meet at a point to produce a resultant intensity $5 \, W/m^2$. The phase difference between the two waves is ......

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