Two waves of the same frequency and same ampl | vedclass

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

Question

(B) The resultant amplitude $A$ of two waves with amplitudes $A_1$ and $A_2$ and phase difference $\phi$ is given by the formula: $A = \sqrt{A_1^2 + A

Vedclass · Accepted Answer

$2\pi / 3$

Vedclass · Answer

(B) The resultant amplitude $A$ of two waves with amplitudes $A_1$ and $A_2$ and phase difference $\phi$ is given by the formula: $A = \sqrt{A_1^2 + A_2^2 + 2A_1A_2 \cos \phi}$.Given $A_1 = A_2 = a$ and the resultant amplitude $A = a$.Substituting these values into the formula: $a = \sqrt{a^2 + a^2 + 2a^2 \cos \phi}$.Squaring both sides: $a^2 = 2a^2 + 2a^2 \cos \phi$.Dividing by $a^2$: $1 = 2 + 2 \cos \phi$.Rearranging gives: $2 \cos \phi = -1$,so $\cos \phi = -1/2$.Therefore,the phase difference $\phi = 120^\circ$ or $\phi = 2\pi / 3$ radians.

Two waves of the same frequency and same amplitude $a$ are superimposed. If the resultant amplitude is also $a$,what is the phase difference between the two waves?

Similar Questions

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 ......

What is interference? Define its types.

The equations of motion for two waves traveling in the same direction are given by ${y_1} = A\sin (\omega t - kx)$ and ${y_2} = A\sin (\omega t - kx - \theta )$. The resultant amplitude of the medium particle will be

Two waves have the same amplitude $A$ and the same frequency $\omega$. If the phase difference between them is $\pi / 2$,what are the resultant amplitude and the resultant frequency when they superimpose at a point?

Vedclass Test Series

Exam Paper Generator

Online Exam Module