Transverse Wave Velocity

[Shjanzey]

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I am struggling with the following concept

Increasing which of the following will increase the speed at which a transverse wave travels on a rope.

A) Wavelength
B) Linear Density
C) Tension
D) Period

I chose A) Wavelength, because of the relationship

velocity = frequency * wavelength

However the answer said it is C) tension because of the relationship

velocity = sqrt(tension) / sqrt(linear density)

How do these two equations relate to each other, and I why am I so drastically wrong?

 

[milski]

v=fλ gives you the relation between the frequency and the wavelength for a given speed of propagation of the wave. The speed of the wave is property of the media and does not depend on the frequency/wavelength. Trying to change the wavelength will result in a change of the frequency or vice versa when the media stays the same.

 

[Shjanzey]

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