The displacement at a point due to two waves | vedclass

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

Question

(B) Given wave equations are $y_1 = 4 \sin(500 \pi t)$ and $y_2 = 2 \sin(506 \pi t)$.Comparing with $y = A \sin(2 \pi f t)$,we get frequencies $f_1 =

Vedclass · Accepted Answer

$3$ beats per second with intensity relation between maxima and minima equal to $9$

Vedclass · Answer

(B) Given wave equations are $y_1 = 4 \sin(500 \pi t)$ and $y_2 = 2 \sin(506 \pi t)$.Comparing with $y = A \sin(2 \pi f t)$,we get frequencies $f_1 = \frac{500 \pi}{2 \pi} = 250 \, Hz$ and $f_2 = \frac{506 \pi}{2 \pi} = 253 \, Hz$.Beat frequency is given by $f_b = |f_2 - f_1| = |253 - 250| = 3 \, Hz$.This means $3$ beats per second are produced.The amplitudes are $A_1 = 4$ and $A_2 = 2$.The intensity $I$ is proportional to the square of the amplitude $(I \propto A^2)$.The ratio of maximum intensity to minimum intensity is given by $\frac{I_{\max}}{I_{\min}} = \frac{(A_1 + A_2)^2}{(A_1 - A_2)^2}$.Substituting the values: $\frac{I_{\max}}{I_{\min}} = \frac{(4 + 2)^2}{(4 - 2)^2} = \frac{6^2}{2^2} = \frac{36}{4} = 9$.Thus,the result is $3$ beats per second with an intensity ratio of $9$.

The displacement at a point due to two waves are $y_1 = 4 \sin(500 \pi t)$ and $y_2 = 2 \sin(506 \pi t)$. The result due to their superposition will be

Similar Questions

Two sound waves having displacements $x_1 = 2 \sin(1000 \pi t)$ and $x_2 = 3 \sin(1006 \pi t)$,when interfere,produce

Two harmonic waves moving in the same direction superimpose to form a wave $x = a \cos(1.5 t) \cos(50.5 t)$ where $t$ is in seconds. Find the period with which they beat (close to the nearest integer). (in $s$)

$A$ tuning fork of frequency $480 \ Hz$ produces $10$ beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces fewer beats per second than before?

$A$ sound wave travels with a velocity of $300 \, m \, s^{-1}$ through a gas. $9$ beats are produced in $3 \, s$ when two waves pass through it simultaneously. If one of the waves has a wavelength of $2 \, m$, the wavelength of the other wave is ..... $m$.

When two tuning forks $A$ and $B$ are sounded together, $4$ beats per second are heard. The frequency of the fork $B$ is $384 \,Hz$. When one of the prongs of the fork $A$ is filed and sounded with $B$, the beat frequency increases. Then the frequency of the fork $A$ is: (in $\,Hz$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module