Wave Velocity

The wave velocity is, not surprisingly, the speed and direction in which the wave travels.

As in other instances of velocity, it is denoted $v$ and has standard SI unit meters per second.

The single most important formula concerning the velocity of a wave is the following: $$v=\lambda f$$ This states that the velocity of a wave is the product of its wavelength and its frequency.

To show that this is true, note that every time a wave makes a full oscillation, it travels a distance $\lambda$.

Suppose that it makes $N$ oscillations in a time $t$. Let the distance be $d$.

The distance traveled is clearly $d=\lambda N$.

Thus, the speed is $v=\frac{d}{t}=\frac{\lambda N}{t}$.

By the definition of frequency, $f=\frac{N}{t}$.

Thus, it is clear that $v=\lambda f$.