A harmonic wave moving in the positive x direction has an amplitude of 2.5 cm, a

Question

A harmonic wave moving in the positive x direction has an amplitude of 2.5 cm, a speed of 37.0 cm/s, and a wavelength of 54.0 cm. Assume that the displacement is zero at x = 0 and t = 0. a. Calculate the displacement (in cm) due to the wave at x = 0.0 cm, t = 2.0 s b. Calculate the displacement due to the wave at x = 10.0 cm, t = 20.0 s

Explanation / Answer

The wave equation is y=Asin(wt-kx) k=2*pi/lambda k=2*pi/0.54=11.63 speed=0.37 and 0.37=f*lambda===>f=0.37/0.54=0.685 ==>w=2*pi*f=4.305 A=0.025 ==>y=0.025sin(4.305t-11.63x) Displacement due to wave at 2 seconds ==>y=0.025*sin(4.305*2)=0.018 Displacement at x=0.1,t=20 ==>y=0.025*sin(4.305*20-11.63*0.1)=-0.002

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