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

Question

A transverse mechanical wave is traveling along a string lying along the x-axis. The displacement of the string as a function of position and time, y(x,t), is described by the following equation: y(x, t) = 0.0350 xsin(3.40x-124t) where x and y are in meters and the time is in seconds What is the wavelength of the wave Tries 0/12 What is the velocity of the wave (Define positive velocity along the positive x-axis.) Tries 0/12 What is the maximum speed in the y-direction of any piece of the string (Give a positive answer for speed.) Tries 0/12

Explanation / Answer

general eqn Y(x,t) = A sin(kx- wt)

k is wave no. = 2pi/L

L is wavelength

W is ang velocity = 2pif

so

here now by comparision

K = 2pi/L = 3.4

wavelength L = 2pi/3.4

L = 1.847 m

-------------------------------

W = 2pif = 124

f = 124/2pi = 19.73 Hz

so   

velocity V = Lf

V = 1.847 *19.73

V = 36.44 m/s

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Vmax = A/t

Vmax = AW

Vamx = 0.035 * 124

Vmax = 4.34 m/s

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