Three waves of equal frequency having amplitu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the amplitudes be $A_1 = 10 \,\mu m$,$A_2 = 4 \,\mu m$,and $A_3 = 7 \,\mu m$. The waves arrive with successive phase differences of $\frac{\pi

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(C) Let the amplitudes be $A_1 = 10 \,\mu m$,$A_2 = 4 \,\mu m$,and $A_3 = 7 \,\mu m$. The waves arrive with successive phase differences of $\frac{\pi}{2}$. Let the phase of the first wave be $0$,the second be $\frac{\pi}{2}$,and the third be $\pi$. Using the phasor method,the resultant amplitude $A_R$ is given by the vector sum of the amplitudes: $A_R = \sqrt{(\sum A_i \cos \phi_i)^2 + (\sum A_i \sin \phi_i)^2}$ $A_x = A_1 \cos(0) + A_2 \cos(\frac{\pi}{2}) + A_3 \cos(\pi) = 10(1) + 4(0) + 7(-1) = 10 - 7 = 3 \,\mu m$ $A_y = A_1 \sin(0) + A_2 \sin(\frac{\pi}{2}) + A_3 \sin(\pi) = 10(0) + 4(1) + 7(0) = 4 \,\mu m$ Resultant amplitude $A_R = \sqrt{A_x^2 + A_y^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \,\mu m$.

Three waves of equal frequency having amplitudes $10 \,\mu m, 4 \,\mu m$ and $7 \,\mu m$ arrive at a given point with successive phase difference of $\frac{\pi}{2}$. The amplitude of the resulting wave in $\mu m$ is given by

Similar Questions

Two pulses on a string approach each other at speeds of $1 \ m/s$. What is the shape of the string at $t = 3 \ s$ :-

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:

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

The similarity between sound and light waves is:

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module