What multiplicative factor does speed and wavelength change by?

[Emmanuel0]

Consider a wave on a string with constant tension. If the frequency of the wave is doubled, by what multiplicative factor does a) the speed and b) the wavelength change?

I don't really know how to begin to answer this question. The best i could think of is using
v=wavelength x f and then putting a square route on the f (frequency) and solving for wavelength and i guess v (speed of the wave) from there.

If anyone know where i can find more problems like this (aside from my textbook) let me know as i am really struggling with this and i want to get a better understanding of it.

 

[vela]

What other equations do you have that apply to a wave on a string?

 

[Emmanuel0]

What other equations do you have that apply to a wave on a string?

v= square root(F/U)

 

[vela]

Good, so that's where F is the tension in the string and $\mu$ is its mass per unit length. How do the wavelength and frequency affect those quantities, if at all?

 

[Emmanuel0]

Good, so that's where F is the tension in the string and $\mu$ is its mass per unit length. How do the wavelength and frequency affect those quantities, if at all?

I am not sure, increasing tension shortens wavelength.

 

[vela]

You might find it useful to play around with this simulation.

http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html

Set the damping to 0 and the end of the string to "no end." Then set the left end oscillate. You can adjust the frequency and tension in the string and see what happens.

I would suggest first leaving the frequency fixed and playing around with the tension. See what happens to the speed and wavelength of the wave.

Then try the opposite. Leave the tension fixed and vary the frequency. What happens to the speed and wavelength of the wave?