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?

6.88 s

Explanation:

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

where v is the wave speed and the wavelength.

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

The amplitude of the wave is

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:

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:

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