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Problem 15.11 ㎜Revew l Constants I Penoic Table Part A (Figure 1) is a snapshot graph of a wave at t 2s What is the maximum speed reached by a particle on the string? Express your answer with the appropriate units. partickh Value Units Figure 1 of 1 Request Answer Provide Feedback y (cm) m/s x (m) -1 1 23 4 5 6 7 0 Type here to search

Answer 1

At $x=0\,m$ the particle has zero displacement $y=0\,cm$

At  $x=1\,m$ the particle has displacement $y=-1\,cm$

Velocity of wave is $\frac{dx}{dt}=1\,m/s$ ,

i) Time taken by wave to move from $x=0\,m$ to $x=1\,m$ is  $1\,s$.

In this time, the displacement of particle is $-1\,cm$ , so particle's velocity is $v_{particle}=\frac{|dy|}{dt}=\frac{1}{1}=1\,cm/s$

ii) Time interval between  $x=1\,m$ to $x=5\,m$ is  $4\,s$.

In this time, the displacement of particle is $2\,cm$ , so particle's velocity is $v_{particle}=\frac{|dy|}{dt}=\frac{2}{4}=0.5\,cm/s$

That is , The particle's velocity from $x=0\,m$ to $x=1\,m$ is $v_{particle}=1\,cm/s$

The particle's velocity from $x=1\,m$ to $x=5\,m$ is $v_{particle}=0.5\,cm/s$

The particle's velocity from $x=5\,m$ to $x=6\,m$ is $v_{particle}=1\,cm/s$   

Hence, maximum velocity of particle is  $(v_{particle})_{max}=1\,cm/s=0.01\,m/s$