The speed of a transverse wave on a string is 450 m/s, and the wavelength is 0.1

Question

The speed of a transverse wave on a string is 450 m/s, and the wavelength is 0.18 m. The amplitude of the wave is 2.0 mm. How many seconds are required for a particle of the string to move through a total distance of 1.0 km?

Explanation / Answer

For any transverse wave we have the condition v = n * (wavelength) so substituting the values we get:- 450 = frequency * (0.18) => frequency = 2500 Hz Frequency means cycle per second .Therefore, frequency 2500 Hz means 2500 cycles per second. A point on string will go nowhere, but will vibrate perpendicular to the velocity of the transverse wave. The amplitude is given in the question as 2.0 mm. In one cycle a particle (on string) travels a distance of 4*(amplitude). so ,in our question one cycle a particle (on string) travels a distance of 4*2.0mm = 8mm . we have frequency of 2,500 cycles per second.Therefore, covering in all 2,500* 8mm = 20,000 mm = 20 m in 1 second. Using the same relation we can get the time to cover a distance of 1Km for the particle on the string as 50 seconds. Final answer :---- time required for a particle of the string to move through a total distance of 1.0 km? Is t= 50 seconds.

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