What is the maximum magnitude of the transverse speed of the string?

In summary, the wave function for a traveling wave on a taut string is given by y(x, t) = (0.12 m)sin(6πt - 3πx + π/4) in SI units. The question is asking for the maximum magnitude of the transverse speed of the string. It is unclear whether this refers to the speed at the highest point or the amplitude. The equation A x V is suggested as a possible solution, but it is unclear how to use it in this context.
  • #1
ken62310
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Homework Statement


The wave function for a traveling wave on a taut string is (in SI units) the following equation.

y(x, t) = (0.12 m)sin(6πt - 3πx + π/4)
What is the maximum magnitude of the transverse speed of the string.

I don't quite understand the question.
Does it mean the speed of the string when it reached the highest point?
or it is asking for the amplitude?

does this solve the problem? A x V?
or I should sub in the A into the x in order to get the time t and then solve for the speed?
 
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  • #2
Homework Equationsy(x, t) = (0.12 m)sin(6πt - 3πx + π/4)The Attempt at a SolutionI'm not sure how to solve this problem.
 

Related to What is the maximum magnitude of the transverse speed of the string?

What is the maximum magnitude of the transverse speed of the string?

The maximum magnitude of the transverse speed of the string is determined by the tension and density of the string, as well as the frequency and wavelength of the wave traveling through it. It is also affected by any external forces acting on the string.

How is the maximum magnitude of the transverse speed calculated?

The maximum magnitude of the transverse speed can be calculated using the equation v = √(T/μ), where v is the speed, T is the tension, and μ is the linear density of the string.

What factors can affect the maximum magnitude of the transverse speed?

The tension and density of the string are the main factors that affect the maximum magnitude of the transverse speed. Other factors that can have an impact include the frequency and wavelength of the wave, as well as any external forces acting on the string.

Is there a limit to the maximum magnitude of the transverse speed?

Yes, there is a limit to the maximum magnitude of the transverse speed, as it is ultimately determined by the properties of the string. However, the speed can be increased by increasing the tension or decreasing the density of the string.

Can the maximum magnitude of the transverse speed be exceeded?

No, the maximum magnitude of the transverse speed cannot be exceeded as it is determined by the physical properties of the string. However, the actual speed of the string may be lower due to factors such as friction and damping.

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