The equations of two waves are given byy_{1}= | vedclass

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

Question

(A) Given amplitudes are $A_{1} = 5 \, cm$ and $A_{2} = 3 \, cm$.The phase difference $\Delta \phi$ between the two waves is determined by the differe

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) Given amplitudes are $A_{1} = 5 \, cm$ and $A_{2} = 3 \, cm$.The phase difference $\Delta \phi$ between the two waves is determined by the difference in their arguments:$\Delta \phi = 2 \pi (x - vt + 1.5) - 2 \pi (x - vt) = 2 \pi (1.5) = 3 \pi$.The resultant amplitude $A_{net}$ is given by the formula:$A_{net} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos(\Delta \phi)}$.Substituting the values:$A_{net} = \sqrt{5^{2} + 3^{2} + 2(5)(3) \cos(3 \pi)}$.Since $\cos(3 \pi) = -1$:$A_{net} = \sqrt{25 + 9 + 30(-1)} = \sqrt{34 - 30} = \sqrt{4} = 2 \, cm$.

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.........$cm$.

Similar Questions

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

The resultant amplitude due to the superposition of two waves $y_1 = 5 \sin (\omega t - kx)$ and $y_2 = -5 \cos (\omega t - kx - 150^{\circ})$ is:

Two waves are represented by $y_1 = a \sin(\omega t + \frac{\pi}{6})$ and $y_2 = a \cos(\omega t)$. What will be their resultant amplitude?

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

The amplitude of the resultant wave produced by the superposition of two waves $y_1 = A_1 \sin(wt - \beta_1)$ and $y_2 = A_2 \sin(wt - \beta_2)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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$.