Question

At t = 0 the end you are oscillating is at its maximum positive displacement and is instantaneously at rest. Write an equation for the displacement as a function of time at a point 2.50 m from that end. Assume that no wave bounces back from the other end. Express your answer in millimeters in terms of t.

Answer 1

Answer:

The equation of displacement is $y=A\sin(\omega t-2.50 k+\dfrac{\pi}{2})$.

Explanation:

Given that,

Distance = 2.50 m

We need to calculate the equation of wave

Using general equation of wave

$y=A\sin(\omega t-kx+\phi)$....(I)

Where, A = amplitude

t = time

x = displacement

$\phi$ = phase difference

Put the value in the equation

At t = 0, x = 0, y =A

$A=A\sin(0+\phi)$

$\sin\phi=1$

$\phi=\dfrac{\pi}{2}$

From equation (I)

$y=A\sin(\omega t-2.50 k+\dfrac{\pi}{2})$

Hence, The equation of displacement is $y=A\sin(\omega t-2.50 k+\dfrac{\pi}{2})$.