A transverse wave on a string is described by the following wave function. where

Question

A transverse wave on a string is described by the following wave function. where x and y are in meters and t is in seconds. Determine the transverse speed at t = 0.180 s for an element of the string located at x = 1.30 m. Given the equation for the vertical position of elements of the string as a function of time, how do you determine the velocity of those elements as a function of time? m/s Determine the transverse acceleration at t = 0.180 s for an element of the string located at x = 1.30 m. Given the equation for the vertical position of elements of the string as a function of time, how do you determine the velocity of those elements as a function of time? m/s2 What is the wavelength of this wave? What is the period of this wave? What is the speed of propagation of this wave?

Explanation / Answer

(a) y = 0.100 sin(pi*1.30/12 + 5pi t) so

speed = 0.100 cos(0.34034 + 5pi t) * 5pi =

= 0.100 cos(0.34034 + 5pi*0.180) *5pi = -1.57 m/s (but they might want just 1.57)

(b) acc = -0.100 * 5pi * 5pi sin(0.34034 + 5pi*0.180) =

= 0.6461 m/s^2

(c) wavelength = 2pi/k = 2pi / (pi/12) = 24 m

(d) period = 2pi / w = 2pi / 5pi = 0.400 s

(e) speed = wavelength / period = 24 / 0.4 = 60 m/s

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