Understanding Wave Frequency and Tension: V=fλ vs V=√T/μ

[tanzl]

Homework Statement

I do not understand the difference between v=f \lambda and v=\sqrt{T/\mu}
If a string is vibrated twice the frequency but the same tension as previous. Would the speed of the wave doubled?

 

[LowlyPion]

One equation relates the physical relationship of the wave - frequency, wavelength to velocity of propagation.

The other relates the velocity to the physical properties of the transmission media Tension and mass/length to the velocity of propagation.

Which properties can affect the speed of propagation? If you change the frequency of the wave how would you have affected the properties of the media that determine speed of propagation?

 

[davieddy]

If a string is vibrated twice the frequency but the same tension as previous. Would the speed of the wave doubled?

No. Yhe wacelength would be halved.

 

[tanzl]

If the both equations are true for the string. The only way to have same tension and thus same speed but different frequency would be a different wavelength. But, that is from equation. How can I prove it or derive it? or maybe a more concrete example. Thanks.

 

[davieddy]

A train has many trucks, each L metres long. If f trucks pass per second,
how fast is the train going?

 

[tanzl]

v=Lf
L is wavelength and f is frequency.
I understand this equation but I confused the two.
In your example, if I increase f the speed will increase but it is not the case in a string.
I am not convinced that by doubling the frequency of the vibration the speed of the wave is still the same.

 

[LowlyPion]

The point is that changing the frequency changes no property of the wire, and it is the physical property of the wire that determines the speed of propagation. Namely force and mass distribution.

The statement says Tension is the same. Same wire. Same mass per length. Same velocity of propagation.

Hence the only thing that can change if you change frequency is λ.

 

[davieddy]

I have posted a nifty derivation of v^2 = T/m in the classical physics forum

https://www.physicsforums.com/showthread.php?t=288922