Question

A pulse can be described as a single wave disturbance that moves through a medium. Consider a pulse that is defined at time t = 0.00 s by the equation y(x) = 6.00 m³/(x² + 2.00 m²) centered around x = 0.00 m. The pulse moves with a velocity of v = 3.00 m/s in the positive x-direction.
(a) What is the amplitude of the pulse?
(b) What is the equation of the pulse as a function of position and time?
(c) Where is the pulse centered at time t = 5.00 s?

Answer 1

Answer:

a)A= 3 m

b)$y(x)=\dfrac{6}{(x-3t)^2+2}\ m$

c)D= 15 m

Explanation:

Given that

$y(x)=\dfrac{6}{x^2+2}\ m$

v= 3 m/s

a)

The amplitude(A) of the pulse :

When x= 0 ,Then y = A

Put x= 0  

$y(x)=\dfrac{6}{x^2+2}\ m$

$y(0)=\dfrac{6}{0^2+2}\ m$

y= A= 3 m

A= 3 m

b)

Distance travel in time t  

x= vt

x= 3 t

$y(x)=\dfrac{6}{(x-3t)^2+2}\ m$

c)

The distance covered by pulse in the time 5 s

D = v t

D= 3 x 5  

D= 15 m