The equation of a wave travelling on a string | vedclass

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

Question

(A) The general equation of a wave is $y = A \sin(kx + \omega t + \phi)$.Comparing this with the given equation $y = \sin(20 \pi x + 10 \pi t)$,we get

Vedclass · Accepted Answer

$5.0$

Vedclass · Answer

(A) The general equation of a wave is $y = A \sin(kx + \omega t + \phi)$.Comparing this with the given equation $y = \sin(20 \pi x + 10 \pi t)$,we get the wave number $k = 20 \pi \ rad/m$.The wavelength $\lambda$ is given by $\lambda = \frac{2 \pi}{k} = \frac{2 \pi}{20 \pi} = 0.1 \ m = 10 \ cm$.Points having the same oscillating speed in a wave are separated by a distance of $\frac{\lambda}{2}$ (or multiples thereof).Therefore,the minimum distance is $\frac{\lambda}{2} = \frac{10 \ cm}{2} = 5 \ cm$.

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 $cm$)

Similar Questions

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 half the wave velocity,if $c=$

Write the definition of the time period of a wave.

Give the definition,$SI$ unit,and dimensional formula of the time period,angular frequency,and frequency of a wave.

$A$ transverse harmonic wave on a string is given by $y(x, t) = 5 \sin (6t + 0.003x)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The wave velocity is $...........\,ms^{-1}$.

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$. This represents:

Vedclass Test Series

Exam Paper Generator

Online Exam Module