Question

1. You are playing with a jump rope that is tied at both ends. You untie one end, hold it taut and wiggle the end up and down sinusoidally with frequency 2.00Hz and amplitude 0.075m. At time t=0, the end has a maximum positive displacement and is instantaneously at rest. Assume no wave bounces back from the far end to change the pattern. What is the equation for the displacement of the wave? What is the displacement at a point 3.00m from the end .

Answer 1

`f(x=3.00m)=0.075mcos((2\pi(2.00Hz))/(v)(3.00m))`

Step-by-step explanation:

To find the equation of the wave you use the general equation for a wave, given by:

`f(x)=Acos(k x-\omega t)`

A: amplitude of the wave = 0.075m

k: wave number

you select a cosine function because for x=0 and t= 0 you get a maximum displacement.

To find the displacement of the wave for x=0 you can consider that the form of the wave is independent of time t.

Then, you calculate k:

`k=(\omega)/(v)=(2\pi f)/(v)`

Thus, you need the value of the speed of the wave (you only have the frequency f), in order to calculate f(x), for x=3.00m:

`f(x=3.00m)=0.075mcos((2\pi(2.00Hz))/(v)(3.00m))`