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

Question

A transverse mechanical wave istraveling along a string lying along the x-axis. The displacementof the string as a function of position and time, y(x,t), isdescribed by the following equation:
y(x,t)=0.0400*sin(7.00x-168t),
where x and y are in meters and the time is in seconds.

a- What is the wavelength of the wave? b- What is the velocity of thewave? (Define positive velocity along the positive x-axis.) c-What is the maximum speed in they-direction of any piece of the string? (Give a positive answer forspeed.) A transverse mechanical wave istraveling along a string lying along the x-axis. The displacementof the string as a function of position and time, y(x,t), isdescribed by the following equation:
y(x,t)=0.0400*sin(7.00x-168t),
where x and y are in meters and the time is in seconds.

a- What is the wavelength of the wave? b- What is the velocity of thewave? (Define positive velocity along the positive x-axis.) c-What is the maximum speed in they-direction of any piece of the string? (Give a positive answer forspeed.)

Explanation / Answer

Given that The displacement of the string is         y(x,t)=0.0400*sin(7.00x-168t) a) The wavelength of the wave is                   = 2/k                      =2/(7.00 rad/m)    b) The velocity of the wave is                         v=/k                           = (168 rad/s)/(7.00 rad/m)   c) The maximum speed in the y-direction of any piece ofthe string is                   vmax = (0.0400 m)(168 /s) Simplifying we get the answer.                           = (168 rad/s)/(7.00 rad/m)   c) The maximum speed in the y-direction of any piece ofthe string is                   vmax = (0.0400 m)(168 /s) Simplifying we get the answer.

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