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

Question

A transverse mechanical wave is traveling along a string lyingalong the x-axis. The displacement of the string as a function ofposition and time, y(x,t), is described by the following equation:y(x,t)=0.0460*sin(3.20x - 164t)
where x and y are in meters and the time is in seconds.

What is the wavelength of the wave? and,,,,, What is the velocity of the wave? (Define positive velocityalong the positive x-axis.)
A transverse mechanical wave is traveling along a string lyingalong the x-axis. The displacement of the string as a function ofposition and time, y(x,t), is described by the following equation:y(x,t)=0.0460*sin(3.20x - 164t)
where x and y are in meters and the time is in seconds.

What is the wavelength of the wave? and,,,,, What is the velocity of the wave? (Define positive velocityalong the positive x-axis.)

Explanation / Answer

    y ( x, t ) = 0.0460 * sin ( 3.20 x -164 t ) .................(1)     General equation of a transversemechanical wave is,     y ( x, t ) = A sin ( k x - t ) ....................................(2)     Where y ( x , t ) = Displacement as a functionof time                          A = Amplitude of the wave                          k = propagation constant = 2 /                          = Angular frequency                         t = time (a)     By comparing equ. (1) and (2)     k = 3.20     Wavelength, = 2 / k                          = 2 / 3.2                          = 1.9625 m                          = 1.96 m (b)     Angular frequency, = 164     Wave velocity, V = / k                               = 164 / 3.2                               = 51.25 m/s

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