The equation of a progressive wave is given b | vedclass

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

Question

(C) The standard equation for a progressive wave is $x = A \sin(\omega t + ky)$.Comparing the given equation $x = 1.2 \sin(314t + 12.56y)$ with the st

Vedclass · Accepted Answer

$0.5 \, m, -ve \, y$-direction

Vedclass · Answer

(C) The standard equation for a progressive wave is $x = A \sin(\omega t + ky)$.Comparing the given equation $x = 1.2 \sin(314t + 12.56y)$ with the standard form,we get the wave number $k = 12.56 \, 	ext{rad/m}$.The wavelength $\lambda$ is given by the formula $\lambda = \frac{2\pi}{k}$.Substituting the value of $k$ and $\pi \approx 3.14$:$\lambda = \frac{2 	imes 3.14}{12.56} = \frac{6.28}{12.56} = 0.5 \, 	ext{m}$.Since the term inside the sine function is $(314t + 12.56y)$,the positive sign between the $t$ and $y$ terms indicates that the wave is traveling in the negative direction of the axis associated with the variable $y$.Therefore,the wave is traveling in the $-ve \, y$-direction.

The equation of a progressive wave is given by $x = 1.2 \sin(314t + 12.56y)$. What are the wavelength and the direction of the wave?

Similar Questions

Which of the following expressions represents a simple harmonic progressive wave?

$A$ progressive wave of frequency $50 \,Hz$ is travelling with velocity $350 \,m/s$ through a medium. The change in phase at a given time interval of $0.01 \,s$ is

For a progressive wave given by the equation $y = 4 \sin \frac{\pi}{2} (8t - \frac{x}{8}) \, cm$,what is the wave velocity and its direction?

$A$ progressive wave of frequency $500 \,Hz$ is travelling with a velocity of $360 \,ms^{-1}$. The distance between two points, having a phase difference of $60^{\circ}$, is ............. (in $\,m$)

$A$ progressive wave of frequency $400 \ Hz$ is travelling with velocity $336 \ m/s$. How far apart are the two points on a wave which are $60^{\circ}$ out of phase (in $m$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module