A transverse mechanical wave is traveling along astring lying along the x-axis.

Question

A transverse mechanical wave is traveling along astring lying along the x-axis. The displacement of the string as afunction of position andtime, y(x,t), is described by thefollowing equation:

y(x,t)=0.0380×sin(6.00x144t)
where x and y are in meters and the time is in seconds
What is the wavelength of the wave?
What is the velocity of the wave? (Define positivevelocity along the positive x-axis.)
What isthe maximum speed in the y-direction of any piece of the string?(Give a positive answer for speed.)
y(x,t)=0.0380×sin(6.00x144t)

Explanation / Answer

Given that a transverse mechanical wave istraveling along a string lying along the x-axis                                  y(x,t)=0.0380×sin(6.00x144t) Comparing the above equation with the y (x,t)=Asin(kx-t) From the above equations we get that A = 0.0380m k = 6.00 =144 Now wavelength of the wave is given by              k = 2/              6.00 =2/ a) Then the wavelength () = 2/6                                     = 6.28/6                                     = 1.0467m b) Now the speed of the wave is given by               v= /k                  =144/6                  =24m/s c) The maximum speed in the y-direction of anypiece of the string is             vmax = A                    = (0.0380m)(144s-1)                    = 5.472m/s y(x,t)=0.0380×sin(6.00x144t)

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