A simple harmonic progressive wave is represe | vedclass

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

Question

(D) The given wave equation is $Y = A \sin 2 \pi (n t - \frac{x}{\lambda})$.Comparing this with the standard wave equation $Y = A \sin (\omega t - kx)

Vedclass · Accepted Answer

$\pi A$

Vedclass · Answer

(D) The given wave equation is $Y = A \sin 2 \pi (n t - \frac{x}{\lambda})$.Comparing this with the standard wave equation $Y = A \sin (\omega t - kx)$,we have $\omega = 2 \pi n$ and $k = \frac{2 \pi}{\lambda}$.The maximum particle velocity is given by $v_{p, 	ext{max}} = A \omega = A (2 \pi n)$.The wave velocity is given by $v_w = \frac{\omega}{k} = \frac{2 \pi n}{2 \pi / \lambda} = n \lambda$.According to the problem,$v_{p, 	ext{max}} = 4 v_w$.Substituting the expressions,we get $A (2 \pi n) = 4 (n \lambda)$.Simplifying the equation,$2 \pi A n = 4 n \lambda$.Dividing both sides by $2n$,we get $\lambda = \pi A$.

$A$ simple harmonic progressive wave is represented as $Y = A \sin 2 \pi (n t - \frac{x}{\lambda}) \text{ cm}$. If the maximum particle velocity is four times the wave velocity,then the wavelength of the wave is

Similar Questions

$A$ plane progressive wave is given by $y = 2 \cos 6.284(330t - x)$. What is the period of the wave?

Two waves are represented by the equations, $y_1 = a \sin(\omega t + kx + 0.57)$ and $y_2 = a \cos(\omega t + kx)$, where $x$ is in metre and $t$ is in second. What is the phase difference between them? $(\pi = 3.14)$

What is the ratio of the amplitudes of the waves $y_1 = 10 \sin(3\pi t + \frac{\pi}{3})$ and $y_2 = 5[\sin 3\pi t + \sqrt{3} \cos 3\pi t]$?

Velocity of sound waves in air is $V \ m/s$. For a particular sound wave in air,a path difference of $x \ cm$ is equivalent to a phase difference of $n\pi$. The frequency of this wave is:

$A$ progressive sound wave is represented by $y = a \sin(400\pi t - \pi x / 6.85)$,where $x$ is in $m$ and $t$ is in $s$. The frequency of the wave is .... $Hz$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module