2. Transverse waves on a string have a wave speed of 8.00 m/s, amplitude 0.0700

Question

2. Transverse waves on a string have a wave speed of 8.00 m/s, amplitude 0.0700 m, and wavelength 0.320 m. The waves travel in the -x-direction, and at t = 0 the x = 0 end of the string has its maximum upward displacement. a. Find the frequency, period, and wave number of the waves. b. Write a wave function describing the wave. c. Find the transverse displacement of a particle at x = 0.3 60 m at time t = 0.150 s. d. How much time must elapse from the instant in part (c) until the particle at x = 0.3 60 m next has a maximum upward displacement?

Explanation / Answer

a) freuency is given as ::

f = speed/wavelength = 8m/s / 0.32 = 25 Hz

Time period = 1/ frequency = 1/25 = 0.04 sec

wave number = 2pi/wavelength = 2*3.14 / (0.32) = 19.6

d) at t = 0 , Y = maximum

time period = 0.04

so wave has maximum displacement at t = 0, 0.04 , 0.08 , 0.12 , 0.16

time mentioned is 0.15 sec in part c)

so time remaining = 0.16 - 0.15 = 0.01 sec

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