Does phase speed = wave speed, for a wave on a string?

[jumbogala]

Homework Statement

A wave travels along a string. Its amplitude is 0.500 mm, its frequency is 300 Hz, and λ ‎= 0.10 m. μ = 0.01 kg/m.

If I double the tension, but keep the wavelength the same, how would the amplitude and the phase speed of the wave change?

Homework Equations

v = sqrt (T / μ), where T is tension and v is wave speed

v = λ‎f

The Attempt at a Solution

First off - is v in the above equations the same as phase speed!? I can't find any reference in my text to phase speed...

If so calculating the change in phase speed would be easy, just sub the new values into the equations.

But amplitude, I'm not sure. I have no equation for that!

 

[anathema]

Hello! Yes, v in those equations does refer to phase speed. To calculate the change in phase speed, you can simply use the equation v = sqrt(T/μ) and plug in the new tension value (which is double the original tension) and the same value for μ. This will give you the new phase speed.

As for amplitude, there is no direct equation for it, but you can use the equation v = λ‎f to calculate the new frequency of the wave. Then, you can use the equation A = v/2πf to calculate the new amplitude. Since the wavelength and tension remain the same, the only change will be in the frequency, which will result in a change in amplitude. I hope this helps!