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

Answer:

Yes. the wave is a stationary wave

Amplitude=7.91 cm

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=$8sin(4.0\times 2.0)=7.91 cm$