A traveling wave is comprised of a bunch of individual oscillators moving in a seamingly cooperative way such that a new feature arises from the their collective motion.

The velocity for a wave on a string or rope depends on the tension $F^T$ and the mass per length $\mu$.

$v_{string}=\sqrt{\frac{F^T}{\mu}}$

The velocity for a sound wave in a gas depends on the adiabatic constant $\gamma$ (specific to each gas), the gas constant $R$, temperature $T$, and molar mass of the gas $m$. At standard temperature and pressure it has a value of 343 m/s.

$v_{gas}=\sqrt{\frac{\gamma R T}{m}}$

The velocity for light in a vacuum is a constant value.

$v_{light}= 2.998x10^8 m/s$

When a wave travels from one medium to another, like from a light string to a heavy string, the frequency of the wave on both sides of the boundary must be the same. One way to justify this claim is to imagine a point on both sides of the boundary of a light string tied to heavy string. If it's not going up and down at the same rate on both sides of the boundary, the knot holding the strings together will break. This is a way of stating the wave must be continuous. Since the speed changes based on the features of the medium, the wavelength will change as well to satisfy the relationship $v = f \lambda$.

Now, take a look at the pre-lecture reading and videos below.