A wave on a string is described by y(x,t) = 17.5 sin(0.411x - 11.8t) where x and

Question

A wave on a string is described by

y(x,t) = 17.5 sin(0.411x - 11.8t)

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 = 6.79 cm when t = 0.245 s? (b) What is the maximum transverse speed of any point on the string? (c) What is the magnitude of the transverse acceleration for a point on the string at x = 6.79 cm when t = 0.245 s? (d) What is the magnitude of the maximum transverse acceleration for any point on the string?
Give your answers in centimeter-based units.

Explanation / Answer

dy/dt = -17.5*11.8*cos(0.411x - 11.8t) d2y/dt^2 = -17.5*11.8*11.8*sin(0.411x - 11.8t) a)v = dy/dt = -205.462cm/sec b)vmax = 17.5*11.8 = 206.5cm/sec c)a = -244.0157cm/sec^2 d)amax = 2436.7cm/sec^2

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