show that the maximum transverse speed of a particle in the string owing to traveling wave is given by umax=wy and amax=w^2.ym
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Here vv is the speed of the oscillating particle which are moving in the y-direction (transverse) whilst the wave is moving in the x-direction.
All the particles are oscillating with shm in the y-direction with an amplitude AA and a frequency f=2πωf=2πω.
The maximum speed of the particles is ωAωA which happens as they pass their equilibrium position when
y=0=Asin(kx−ωt)⇒kx−ωt=0⇒cos(kx−ωt)=±1y=0=Asin(kx−ωt)⇒kx−ωt=0⇒cos(kx−ωt)=±1.
The speed of the wave in the x-direction is ωkωk.
The gif file shows the wave moving in the x-direction whilst the particle oscillates in the y-direction.
All the particles are oscillating with shm in the y-direction with an amplitude AA and a frequency f=2πωf=2πω.
The maximum speed of the particles is ωAωA which happens as they pass their equilibrium position when
y=0=Asin(kx−ωt)⇒kx−ωt=0⇒cos(kx−ωt)=±1y=0=Asin(kx−ωt)⇒kx−ωt=0⇒cos(kx−ωt)=±1.
The speed of the wave in the x-direction is ωkωk.
The gif file shows the wave moving in the x-direction whilst the particle oscillates in the y-direction.
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