Question

The equation = [(8.0 )(4.0)]cos(1.0) describes a wave generated by a sonometer. State whether or not the wave is a stationary wave and find its amplitude, with given that = 2.0 cm

Answer 1

Yes. the wave is a stationary wave

Amplitude=7.91 cm

Step-by-step explanation:

We are given that an equation

`y=[8.0sin(4.0x)]cos(1.0t)`

We have to find that the given wave is a stationary wave or not and find its amplitude at x=2.0 cm

We know that equation of stationary wave

`y(x,t)=2Asin(kx)cos(\omega t)`

Where

Amplitude=
`2Asin(kx)`

The given equation is of the form of stationary wave equation.

By comparing we get

`2Asin(kx)=8sin(4.0x)`

Substitute the value of x

Therefore, the amplitude of the wave

Amplitude=
`8sin(4.0* 2.0)=7.91 cm`