The equation of a simple harmonic progressive | vedclass

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

Question

(C) The given wave equation is $Y = a \sin(2 \pi b t - 2 \pi c x)$.Comparing this with the standard wave equation $Y = A \sin(\omega t - k x)$,we get

Vedclass · Accepted Answer

$c = \frac{1}{\pi a}$

Vedclass · Answer

(C) The given wave equation is $Y = a \sin(2 \pi b t - 2 \pi c x)$.Comparing this with the standard wave equation $Y = A \sin(\omega t - k x)$,we get angular frequency $\omega = 2 \pi b$ and wave number $k = 2 \pi c$.The maximum particle velocity is given by $(V_{max})_p = \omega A = (2 \pi b) a$.The wave velocity is given by $V_w = \frac{\omega}{k} = \frac{2 \pi b}{2 \pi c} = \frac{b}{c}$.According to the problem,the maximum particle velocity is twice the wave velocity:$(V_{max})_p = 2 V_w$.Substituting the values: $2 \pi b a = 2 \left( \frac{b}{c} \right)$.Dividing both sides by $2b$,we get $\pi a = \frac{1}{c}$,which implies $c = \frac{1}{\pi a}$.

The equation of a simple harmonic progressive wave is given by $Y = a \sin 2 \pi (b t - c x)$. The maximum particle velocity will be twice the wave velocity if:

Similar Questions

Write the definition of wave speed and derive $v = \frac{\omega}{k}$.

$A$ sine wave of wavelength $\lambda$ is travelling in a medium. The minimum distance between two particles,which always have the same speed,is

Which of the following functions for $y$ can never represent a travelling wave?

$A$ 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 motion (with $t$ in seconds and $x$ in metres) is given by $y = 7\sin(7\pi t - 0.4\pi x + \frac{\pi}{3})$. The velocity of the wave will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module