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If wave y=A cos(omega t + kx) moving alo...

If wave `y=A cos(omega t + kx)` moving alongs x-axis the shapes of pulse at t=0 and t=2s.

A

are different

B

are same

C

may not be same

D

none of these

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The correct Answer is:
B
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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 y(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 t , if the wave speed is v .

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Consider two simple harmonic motion along x and y- axis having same frequencies but different amplitudes as x=A sin (omega t+varphi) (along x axis) and y= B sin omega t ( along y axis). then show that (x^(2))/(A^(2))+(y^(2))/(B^(2))-(2xy)/(AB) cos varphi = sin^(2) varphi and also discuss the special cases when varphi=(pi)/(2) and A=B Note : when a particle is subjected to two simple harmonic motion at right angle to each other the particle may move along different paths.

Consider two simple harmonic motion along x and y- axis having same frequencies but different amplitudes as x=A sin (omega t+varphi) (along x axis) and y= B sin omega t ( along y axis). then show that (x^(2))/(A^(2))+(y^(2))/(B^(2))-(2xy)/(AB) cos varphi = sin^(2) varphi and also discuss the special cases when varphi=(pi)/(2) Note : when a particle is subjected to two simple harmonic motion at right angle to each other the particle may move along different paths.

The displacement of particle moving along x-axis is given by x=6t+12t^(2) , calculate the instantaneous velocity at t=0 and t=2s.

A pulse travelling on a string is represented by the function y=a^3/((x-vt)^2+a^2) where a=5 mm and v=20 cms^-1. Sketch the shape of the string at t=0, 1 s and 2s. Take x=0 in the middle of the string.

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