Question

Y(x,t)=0.8/[(4x+5t)2+5] represents a moving pulse where x and y are in metre and t in second. Then

A Pulse is moving in positive x−direction.
B In 2 second, it will travel a distance of 2.5 m
C Its maximum displacement is 0.16 m
D It is a symmetric pulse

Answer 1

The given equation represents a moving pulse in the positive x-direction with a propagation speed of 4/5 m/s. In 2 seconds, the pulse will travel a distance of 1.6 m. The maximum displacement of the pulse is 0.16 m and it is a symmetric pulse.

Step-by-step explanation:

The given equation y(x,t)=0.8/[(4x+5t)2+5] represents a moving pulse in the positive x-direction. This is because the pulse has a positive x coefficient in the denominator of the equation. The propagation speed of the pulse can be determined by comparing the coefficients of x and t. In this case, the coefficient of x is 4 and the coefficient of t is 5, so the propagation speed is 4/5 m/s.

To determine the distance the pulse will travel in 2 seconds, we can use the equation Ax = vAt. Plugging in the values, we get Ax = (4/5 m/s)(2 s) = 1.6 m.

The maximum displacement of the pulse can be found by substituting x=0 and t=0 into the equation. In this case, y(0,0) = 0.8/[(0)2+5] = 0.16 m. Therefore, the maximum displacement of the pulse is 0.16 m.

Since the equation y(x,t) is symmetric about the x-axis (y-axis in this case), the pulse is a symmetric pulse.