Don’t be fooled by this formula. The speed of a wave does not depend on the
frequency or wavelength. It depends on properties of the medium.
Wave Rule #1: All waves of the same type in the same medium have the
same speed.The Skinny on Wave Rule #1
If this doesn’t make sense,
imagine that someone
was whispering it to you
and then yelling it at you.
Which would travel faster?
Neither: they’d both be
moving equally fast, at the
speed of sound.
In this single medium, a
wave’s speed is constant,
and is simply an inverse
relationship between
wavelength λ and
frequency, f.If you move a rope up and down at a certain frequency and then suddenly increase
that frequency, the speed remains unchanged. The wavelength, therefore, decreases.
This makes sense since you are creating more pulses per second, each pulse won’t
have as much time to move down the rope before the next pulse is created. The
pulses are closer together, meaning the wavelength has decreased.
Wave Speed on a Stretched String
We can also derive an equation for the speed of a transverse wave on a stretched
string or rope. Let the mass of the string be m and its length be L; then its linear
mass density (μ) is m/L. If the tension in the string is FT, then the speed of a
traveling transverse wave on this string is given by