Question

A transverse pulse travels to the right along a string at a speed v=2.5 m/s. At the shape of the pulse is given by the function

y(x,0)=0.03 e(-x^2/0.04) cos⁡(20πx)

where x and y are in meters. (i) Determine a formula for the pulse's displacement at any time . (ii) Find the displacement of the pulse of the point x=1 m at time t=0.4 s. (iii) What is the transverse velocity of a point on the string having x=1 m at time t=0.4 s? (iv) Repeat part (ii) assuming that the pulse is moving to the left.

Answer 1

Amplitude of wave is 0.003

Velocity of wave is 2.5

The wave is propagating along x axis as a function of cos

Propagation vector

velocity of wave

ANgular frequency

(i)

Displacement at any time

y(x,0)=0.03 e(-x^2/0.04) cos⁡(20πx+)

y(x,0)=0.03 e(-x^2/0.04) cos⁡(20πx+)

(II)

At x=1, t=0.4

(III)

Differenciating above equation

Velocity at x=1, t=0.4

-0.834