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 are the frequency and amplitude of the wave?

Short Answer

Expert verified

The frequency of the wave is f=15.9Hz

The amplitude of the wave is,2cm.

Step by step solution

01

Given data

The string has a maximum speed of vmax=2m/s

The string has a maximum acceleration ofamax=200m/s2

02

Determination of frequency

The maximum speed can be written by, vmax=Aω

The maximum acceleration can be expressed by, role="math" localid="1648915779642" amax=Aω2

According to the question, we can write,

role="math" localid="1648916465485" amaxvmax=Aω2Aωamaxvmax=ωω=2002ω=100rad/s

03

Determination of amplitude 

The frequency of the wave can be obtained by,

f=ω2πf=100rad/s2πf=15.9Hz

Now, the amplitude of the wave can be determined by the expression of maximum speed,

Aω=vmaxA=vmaxωA=2m/s100rad/sA=0.02mA=2cm

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