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

A pulse can be described as a single wave disturbance that moves through a medium. The amplitude of the pulse is 6.00 m³, and the equation of the pulse as a function of position and time is y(x, t) = 6.00 m³/((x - 3.00 m/s * t)² + 2.00 m²). The pulse is centered at x = 15.00 m at time t = 5.00 s.

Step-by-step explanation:

A pulse can be described as a single wave disturbance that moves through a medium. The amplitude of the pulse is a measurement of how far the medium is displaced momentarily from a position of rest. In this case, the equation for the pulse is y(x) = 6.00 m³/(x² + 2.00 m²), so the amplitude of the pulse is 6.00 m³.

The equation of the pulse as a function of position and time is y(x, t) = 6.00 m³/((x - 3.00 m/s * t)² + 2.00 m²). This equation represents the pulse centered around x = 3.00 m/s * t.

At time t = 5.00 s, the pulse is centered at x = 3.00 m/s * 5.00 s = 15.00 m.

Answer 2

a)A= 3 m

b)
`y(x)=(6)/((x-3t)^2+2)\ m`

c)D= 15 m

Explanation:

Given that

`y(x)=(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)=(6)/(x^2+2)\ m`

`y(0)=(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)=(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