Home
Class 12
PHYSICS
A wave is propagating on a long stretche...

A wave is propagating on a long stretched string along its length taken as the positive x-axis. The wave equation is given as
`y=y_0e^(-(t/T-x/lamda)^(2))`
where `y_0=4mm, T=1.0s and lamda=4cm`.(a) find the velocity of wave. (b) find the function `f(t)` giving the displacement of particle at x=0. (c) find the function g(x) giving the shape of the string at t=0.(d) plot the shape g(x) of the string at t=0 (e) Plot of the shape of the string at t=5s.

Text Solution

Verified by Experts

The wave equation may be written as
`y=y_0 e^(-(1/T^2 {t-x/(lambda//T)}^2`
Comparing it with the general equation
`y=f(t-x/v)` , we get , `v=lambda/T=(6cm)/1.0`=6 cm/sec
(b) The wave equation may be written as
`y=y_0 e^(-(1/T^2 {t-x/(lambda//T)}^2`
Putting x=0 in the given equation
`f(t)=y_0 e^(-(t//T)^2)`
(c ) The wave equation may be written as
`y=y_0 e^(-(1/T^2 {t-x/(lambda//T)}^2`
Putting t= 0 in the given equation
`g(x)=y_0 e^(-(x//lambda)^2)`
(d)
Promotional Banner

Similar Questions

Explore conceptually related problems

A pulse is propagating on a long stretched string along its length taken as positive x-axis. Shape of the string at t = 0 is given by y = sqrt(a^2 - x^2) when |x| lt= a = 0 when |x| gt= a . What is the general equation of pulse after some time 't' , if it is travelling along positive x-direction with speed V?

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

A travelling wave on a long stretched string along the positIve x-axis is given by y = 5mm e^(((T)/(5s) - (x)/(5cm))^2) . Using this equation answer the following questions. The velocity of the wave is

The displacement of A particle at x = 0 of a stretched string carrying a wave in the positive X-direction is given by f(t)=Ae^(-t^2) . The wave speed is V. Write equation of the wave.

A wave pulse is travelling on a string with a speed v towards the positive X-axis. The shape of the string at t = 0 is given by g(x) = A sin(x /a) , where A and a are constants. (a) What are the dimensions of A and a ? (b) Write the equation of the wave for a general time 1, if the wave speed is v.

A travelling wave on a long stretched string along the positIve x-axis is given by y = 5mm e^(((t)/(5s) - (x)/(5cm))^2) . Using this equation answer the following questions. At t = 0, x = 0, the displacement of the wave is

Two pulses travelling in opposite directions along a string are shown for t=0 in the figure. Plot the shape of the string at t= 1.0, 2.0, 3.0, 4.0 and 5.0s respectively .

A wave pulse is travelling along +x direction on a string at 2 m//s . Displacement y (in cm ) of the parrticle at x=0 at any time t is given by 2//(t^(2)+1) . Find (i) expression of the function y=(x,t),i.e., displacement of a particle at position x and time t. Draw the shape of the pulse at t=0 and t=1 s.

A transverse wave propagating along x-axis is represented as y(x,t)= 0.8sin(pi/4-4pit-pi/2x) where x is in meter and t is in second. The velocity of wave is

A travelling wave on a long stretched string along the positIve x-axis is given by y = 5mm e^(((T)/(5s) - (x)/(5cm))^2) . Using this equation answer the following questions. The plot of y and x at t = 10 s is best indicated by