A transverse wave on a string is described by the following wavefunction. y = (0

Question

A transverse wave on a string is described by the following wavefunction. y = (0.100 m) sin[(x/12 +5t)] (a) Determine the transverse speed andacceleration at t = 0.210 sfor the point on the string located at x = 1.20 m.
m/s
m/s2

(b) What are the wavelength, period, and speed of propagation ofthis wave?
m
s
m/s y = (0.100 m) sin[(x/12 +5t)] (a) Determine the transverse speed andacceleration at t = 0.210 sfor the point on the string located at x = 1.20 m.
m/s
m/s2

(b) What are the wavelength, period, and speed of propagation ofthis wave?
m
s
m/s

Explanation / Answer

Given y = (0.100 m) sin[(x/12 +5t)] velocity v = dy / dt
               = 0.1 * 5 cos [ (x/12 + 5t)] velocity at t = 0.21 s and x = 1.2 m is   v = 0.5 cos [ ( *1.2 / 12 ) +5 * 0.21 ]                                                                  =-1.3995 m / s accleration a = dv / dt                     =0.1 * 5 * 5 [ - sin[(x/12 +5t)] ]
                   = 11.2 m / s ^ 2 (b). y = (0.100 m) sin[(x/12 +5t)] compare this with    y = A sin [ k x + t ]   we get k = / 12 = 5 wavelength = 2 / k
                     = 24 m period T = 2 /                =0.4 s speed of propagation of this wave v = / k                                                        = 75 m / s

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