Question

The speed of a transverse wave on a string is 450 m/s, while the wavelength is 0.50 m. The amplitude of the wave is 20.00 cm. How much time is required for a particle of the string to move through a total distance of 5.0 km?

Answer 1

6.88 s

Step-by-step explanation:

First of all, we can find the frequency of the wave, given by:

`f=(v)/(\lambda)=(450 m/s)/(0.50 m)=900 Hz`

where v is the wave speed and
`\lambda` the wavelength.

Then we can find the period of the wave, T, which is the reciprocal of the frequency:

`T=(1)/(f)=(1)/(900 Hz)=0.0011 s`

The amplitude of the wave is

`A=20.0 cm=0.20 m`

and this corresponds to the distance between the maximum displacement of the wave and the equilibrium position. Therefore, the wave covers a total distance of 4A (4 times the amplitude) during one period T:

`d=4A=4(0.20 m)=0.80 m`

and this distance is covered in T = 0.0011 s.

Therefore, the total time needed for the wave to cover a total distance of

d' = 5.0 km = 5000 m

is given by:

`t= (d')/(d)T=(5000 m)/(0.80 m)(0.0011 s)=6.88 s`