Question

A sinusoidal wave travels along a stretched string. A particle on the string has a maximum speed of 2.0 m/s and a maximum acceleration of 200 m/s2. What is the amplitude of the wave?

Answer 1

Answer:

The amplitude of the wave is 0.02 m.

Explanation:

Given that,

Maximum speed = 2.0 m/s

Maximum acceleration = 200 m/s²

We need to calculate the angular frequency

Using formula of angular frequency

$\omega=\dfrac{a_{max}}{v_{max}}$

Put the value into the formula

$\omega=\dfrac{200}{2.0}$

$\omega=100\ rad/s$

We need to calculate the amplitude of the wave

Using formula of velocity

$v_{max}=A\omega$

$A=\dfrac{v_{max}}{\omega}$

Put the value into the formula

$A=\dfrac{2.0}{100}$

$A=0.02\ m$

Hence, The amplitude of the wave is 0.02 m.