Problem: The equation of a transverse wave traveling along a very long string is y = 5.43 sin(0.0246πx+ 8.65πt), where x and y are expressed in centimeters and t is in seconds. Determine(a) the speed, (b) the direction of propagation of the wave and (c) the maximum transverse speed of a particle in the string. (d) What is the transverse displacement at x = 1.77 cm when t = 0.705 s?

FREE Expert Solution

The general equation of a transverse wave is:

y=Asin(kx+ωt)

Speed of the wave:

v=ωk

(a)

Speed, v =  ω/k = 8.65π/0.0246π = 351.6 m/s.

The speed of the wave is 351.6 m/s.

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Problem Details

The equation of a transverse wave traveling along a very long string is y = 5.43 sin(0.0246πx+ 8.65πt), where x and y are expressed in centimeters and t is in seconds. Determine

(a) the speed, (b) the direction of propagation of the wave and (c) the maximum transverse speed of a particle in the string. (d) What is the transverse displacement at x = 1.77 cm when t = 0.705 s?

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Our tutors have indicated that to solve this problem you will need to apply the Waves on a String concept. You can view video lessons to learn Waves on a String. Or if you need more Waves on a String practice, you can also practice Waves on a String practice problems.