A wave on a string is described by, y(x, t) = 12.0 sin(?x/8 - 6?t) where x and y

Question

A wave on a string is described by, y(x, t) = 12.0 sin(?x/8 - 6?t) where x and y are in centimeters and t is in seconds. (a) What is the transverse speed for a point on the string at x = 6.50 cm when t = 0.255 s? m/s (b) What is the maximum transverse speed of any point on the string? m/s (c) What is the magnitude of the transverse acceleration for a point on the string at x = 6.50 cm when t = 0.255 s? m/s2 (d) What is the magnitude of the maximum transverse acceleration for any point on the string? m/s2

Explanation / Answer

a)speed=dy/dt=-72*cos(x/8-6t) at x=6.5 cm and t=0.255 sec speed=-67.41 cm/s b)maximum transverse speed=72 cm/s c)acceleration=dv/dt=-432*sin(x/8-6t) at x=6.5 cm and t=0.255 sec a=151.75 cm/s^2 d)maximum acceleration=432 cm/s^2

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