Answer to Question #309416 in Physics for Kimie

Question #309416

A wave travelling along a string is describe by y(x,t) = 0.35sin(2.75t – 72.5x).


Determine

i. The velocity with which the wave moves along the string


(2 marks)

ii. The displacement of a particle located at x = 21.5 cm and t = 15.5 sec.

(3 marks)


1
Expert's answer
2022-03-10T18:00:43-0500

The general equation of a wave is given by

y(x,t)=Asin(ωtkx)y(x,t) = A\sin(\omega t – k x)

In our case


y(x,t)=0.35sin(2.75t72.5x)y(x,t) = 0.35\sin(2.75t – 72.5x)

i. The velocity with which the wave moves along the string

v=ωk=2.7572.5=0.038m/sv=\frac{\omega}{k}=\frac{2.75}{72.5}=0.038\:\rm m/s

ii. The displacement of a particle located at x = 21.5 cm and t = 15.5 sec

y(0.215,15.5)=0.35sin(2.7515.572.50.215)=0.33my(0.215,15.5) = 0.35\sin(2.75*15.5 – 72.5*0.215)\\ =0.33\:\rm m


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