You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Differential Equation of Wave

The sketch in...

Question

The sketch in the figure shows displacement time curve of a sinusoidal wave at $x = 8 m$ . Taking velocity of wave $v = 6 m / s$ along positive x-axis, write the equation of the wave.

Open in App

Solution

The equation of any wave is $A$ $s i n 2 π (\frac{t}{T} - \frac{x}{λ})$ .
Here the symbols have their usual meaning.
From the figure and the information, we know that
A=0.5m
T=6s $∵$ the wave is repeating every 6 seconds
V=6m/s
x=8cm=0.08m
we know that $λ = \frac{V}{T} = 1 m / s$
The equation now becomes $0.5$ $s i n 2 π (\frac{t}{6} - \frac{0.08}{1})$

Suggest Corrections

Similar questions

Q. A transverse sinusoidal wave moves along a string in the positive

x -

direction at a speed of

10 cm/s

. The wavelength of the wave is

0.5 m

and its amplitude is

10 cm

. At a particular time

t

, the snapshot of the wave is shown in the figure. The velocity of a particle at

P

when its displacement is

5 cm

along

y -

axis is

Q. A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of

10 c m / s

. The wavelength of the wave is

0.5 m

and its amplitude is

10 c m

. At a particular time

t

, the snap-shot of the wave is shown in figure. The velocity of the point

P

when its displacement is

5 c m

is Figure:

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 ?

Q. A wave equation which gives the displacement of particle along

y -

direction is represented as

y = 10^{4} sin (60 t + 2 x)

, where

x

and

y

are in

metre

and

t

sec

. Among the following choose the correct statement.

Q. A wave of wave length

60 m

, amplitude

A = 0.2 m

is moving along positive X-axis with speed

v = 360 m / s

. Equation of wave will be

Join BYJU'S Learning Program

The sketch in the figure shows displacement time curve of a sinusoidal wave at x=8 m. Taking velocity of wave v=6m/s along positive x-axis, write the equation of the wave.

The equation of any wave is A sin2π(tT−xλ).Here the symbols have their usual meaning.From the figure and the information, we know that A=0.5mT=6s ∵ the wave is repeating every 6 secondsV=6m/sx=8cm=0.08mwe know that λ=VT=1m/sThe equation now becomes 0.5 sin2π(t6−0.081)

The sketch in the figure shows displacement time curve of a sinusoidal wave at $x = 8 m$ . Taking velocity of wave $v = 6 m / s$ along positive x-axis, write the equation of the wave.