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)=0.0280*sin(5.40x-150t),
where x and y are in meters and the time is in seconds.

1.What is the wavelength of the wave?

2-What is the velocity of the wave? (Define positive velocity along the positive x-axis.)

3-What is the maximum speed in the y-direction of any piece of the string? (Give a positive answer for speed.)

Explanation / Answer

compare the given equation with

y = A*(sin(w*t-kx)

A = 0.028 m

w = 150 rad/s

k = 5.4 m^-1

a) k = 2*pi/lamda

==> lamda = 2*pi/k

          = 2*pi/5.4

           = 1.163 m

b) v = w/k

      = 150/5.4

       = -27.78 m/s
c) Vmax = A*w = 0.028*150 = 4.2 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.