The equation of a wave is y = 60 sin (1200 t | vedclass

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

Question

(A) The given wave equation is $y = A \sin (\omega t - k x)$,where $A = 60 \ \mu m = 60 	imes 10^{-6} \ m$,$\omega = 1200 \ rad/s$,and $k = 6 \ m^{-1

Vedclass · Accepted Answer

$3.6 	imes 10^{-4}$

Vedclass · Answer

(A) The given wave equation is $y = A \sin (\omega t - k x)$,where $A = 60 \ \mu m = 60 	imes 10^{-6} \ m$,$\omega = 1200 \ rad/s$,and $k = 6 \ m^{-1}$.The maximum particle velocity $(v_p)$ is given by $v_p = A \omega$.$v_p = (60 	imes 10^{-6} \ m) 	imes (1200 \ rad/s) = 72000 	imes 10^{-6} \ m/s = 7.2 	imes 10^{-2} \ m/s$.The wave velocity $(v_w)$ is given by $v_w = \frac{\omega}{k}$.$v_w = \frac{1200}{6} = 200 \ m/s$.The ratio of maximum particle velocity to wave velocity is $\frac{v_p}{v_w} = \frac{A \omega}{\omega/k} = A k$.$\frac{v_p}{v_w} = (60 	imes 10^{-6} \ m) 	imes (6 \ m^{-1}) = 360 	imes 10^{-6} = 3.6 	imes 10^{-4}$.

The equation of a wave is $y = 60 \sin (1200 t - 6 x)$,where '$y$' is in micron,'$t$' is in second,and '$x$' is in metre. The ratio of the maximum particle velocity to the wave velocity of wave propagation is:

Similar Questions

Two waves are represented by the equations $y_1 = A \sin (\omega t + kx + 0.57) \ m$ and $y_2 = A \cos (\omega t + kx) \ m$,where $x$ is in metre and $t$ is in second. What is the phase difference between them?

The equation of a transverse wave travelling along a string is $y(x, t) = 4.0 \sin(20 \times 10^{-3} x + 600 t) \ mm$,where $x$ is in $mm$ and $t$ is in seconds. The velocity of the wave is:

The equation of the propagating wave is $y = 25 \sin (20t + 5x)$,where $y$ is displacement. Which of the following statements is not true?

$A$ longitudinal wave is represented by $x=x_0 \sin 2 \pi(n t-x / \lambda)$. The maximum particle velocity will be four times the wave velocity if:

The equation of a wave travelling on a string is $y = \sin(20 \pi x + 10 \pi t)$,where $x$ and $t$ are distance and time in $SI$ units. The minimum distance between two points having the same oscillating speed is (in $cm$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module