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

Question

A transverse wave on a string is described by the following wave function. y = 0.085 sin (?/12x+3?t) where x and y are in meters and t is in seconds. (a) Determine the transverse speed at t = 0.110 s for an element of the string located at x = 1.50 m. m/s 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 (b) Determine the transverse acceleration at t = 0.110 s for an element of the string located at x = 1.50 m. m/s^2 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 (c) What is the wavelength of this wave? m (d) What is the period of this wave? s (e) What is the speed of propagation of this wave? m/s

Explanation / Answer

a)v=dy/dt

v=0.085*3pi*cos(pi/12x+3pi*t)
b)a=dv/dt
v=dy/dt
we get a=-0.085*3pi*3pi*sin (/12x+3t)
put t= 0.11 and x=1.50 in above formula
c)k=2pi/

we get =1/6

d)period=1/f

w=2pi*f

t=2/3=0.666sec

e)speed=w/k
k=pi/12,w=3pi
v=36m/s

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