The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given f(t) = A sin (t/T). The wave speed is $ν$ . Write the wave equation.

Open in App

Solution

Given,
Equation of the wave travelling in the positive x-direction at x = 0:
$f (t) = A \sin (\frac{t}{T})$
Here,
Wave speed = v
Wavelength, λ = vT
T = Time period
Therefore, the general equation of the wave can be represented by
$y = A \sin [(\frac{t}{T}) - (\frac{x}{ν T})]$

Suggest Corrections

Similar questions

Q. A wave propagates on a string in the positive x-direction at a velocity

ν

. The shape of the string at

t = t_{0}

is given by

g (x, t_{0}) = A \sin (x / a)

. Write the wave equation for a general time t.

Q. A wave travels along the positive x- direction with a speed of

20 m s^{- 1}

.The amplitude of the wave is

0.20 c m

and the wavelength

2.0 c m

.
(a) write a suitable wave equation which describes this wave.
(b) What is the displacement and velocity of the particle at

x = 2.0 c m

at time

t = 0

according to the wave equation written ?

A wave propagates on a string in the positive x-direction at a velocity v. The shape of the string at $t = t_{0}$ is given by $g (x, t_{0})$ = A sin $(\frac{x}{a})$ Write the wave equation for a general time t.

Q. A sinusoidal wave travelling in the positive direction of x on a stretched string has amplitude 2.0 cm, wavelength 1 m and wave velocity 5.0 m/s. At x = 0 and t = 0, it is given that displacement y = 0 and

\frac{\partial y}{\partial t} < 0

. Express the wave function correctly in the from y = f(x, t) :-

Join BYJU'S Learning Program

The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given f(t) = A sin (t/T). The wave speed is ν. Write the wave equation.

Given, Equation of the wave travelling in the positive x-direction at x = 0: ft=AsintT Here, Wave speed = v Wavelength, λ = vT T = Time period Therefore, the general equation of the wave can be represented by y=AsintT-xνT

The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given f(t) = A sin (t/T). The wave speed is $ν$ . Write the wave equation.

Given,
Equation of the wave travelling in the positive x-direction at x = 0:
$f (t) = A \sin (\frac{t}{T})$
Here,
Wave speed = v
Wavelength, λ = vT
T = Time period
Therefore, the general equation of the wave can be represented by
$y = A \sin [(\frac{t}{T}) - (\frac{x}{ν T})]$