Q4 of 97 Page 323

A pulse travelling on a string is represented by the function

,


where a = 5 mm and υ = 20 cm s−1. Sketch the shape of the string at t = 0, 1 s and 2 s. Take x = 0 in the middle of the string.



The maxima in the x-y plane will be the amplitude of the wave.




For maxima, dy/dx=0




So, the amplitude will be,



For velocity in x direction, the function of x and t will be when y=a;




At, t=0;


X=0 cm



At t=1 s


X=20 cm



At t=2 s


X=40 cm



More from this chapter

All 97 →
2

The equation of a wave travelling on a string stretched along the X-axis is given by

.


(A) Write the dimensions of A, a and T. (B) Find the wave speed. (C) In which direction is the wave travelling? (D) Where is the maximum of the pulse located at t = T? At t = 2 T?


 3

Figure (15-E1) shows a wave pulse at t = 0. The pulse moves to the right with a speed of 10 cm s−1. Sketch the shape of the string at t = 1 s, 2 s and 3 s.


 5

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) = A sin(t/T). The wave speed is υ. Write the wave equation.

 6

A wave pulse is travelling on a string with a speed υ toward the position 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 t, if the wave speed is υ.