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:
$y(x,t)=0.0480$×$sin(5.40x-128t)$
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.)

Answer 1

The wavelength of the wave is 1.16m and the velocity is 23.64m/s.

To find the answer, we have to know more about the Transverse waves.

How to find different parameters of a wave?

• The displacement of the string as a function of position and time, y(x,t), when the wave traveling along a string lying along the x-axis is given as,

                $y(x,t)=0.048sin(5.40x-128t)$

• Comparing this with the general form of wave equation, we get,

               $amplitude, a=0.048m\\wave vector, k=5.40\\angular frequency,w=128Hz$

• We have to find the wavelength of the wave, for this, we have the expression as,

                $k=\frac{2\pi }{wavelength} \\\\wavelength=\frac{2\pi }{k} =\frac{2*3.14}{5.40} \\\\wavelength=1.16m$

• We have to find the velocity of the wave,

                         $v=frequency*wavelength\\2\pi f=w, thus,\\f=\frac{w}{2\pi } =\frac{128}{2*3.14}=20.38s^{-1}\\\\v=1.16*20.38=23.64m/s$

Thus, we can conclude that, the wavelength of the wave is 1.16m and the velocity is 23.64m/s

Learn more about the transvers waves here:

brainly.com/question/25746208

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