9.1.3 Wave speed

The speed of a wave refers to the speed at which the energy or momentum is being passed along by the wave. It is different from the speed of the individual particles in the medium as they perform their oscillations (about their equilibrium positions).

Derivation of v=fλ

You can think of wave speed as the speed at which a crest of the wave advances. Do you realize that a crest always advances by one wavelength l after every one period T? Yup, that’s why the speed of the wave is given by the formula

$\displaystyle v=\frac{\lambda }{T}=f\lambda$

In the Same Medium

Do high pitched sound travel faster or slower than low pitched sound? Interestingly, sound waves of different frequency travel at practically the same speed in the same medium. Similarly, light waves have a particular speed in a particular medium that is independent of the wavelength. Since $\displaystyle v=f\lambda$ , and v is a constant, there is an inverse relationship between λ and f.

In Different Mediums

So what determines the speed of a wave? It is the elasticity and inertia of the medium the wave is propagating in. Roughly speaking, the stiffer and lighter the medium particles, the faster the disturbance will be passed along. For example, sound travels faster in solids than gas because solid is a stiffer medium. On the other hand, sound travels faster in helium gas than normal air because helium molecules are lighter.

When a wave crosses from one medium to another, its speed will change (that’s why refraction occurs). This time round, it is the frequency that remains unchanged. Since $\displaystyle v=f\lambda$ , and f is constant, λ is proportional to v.