# Why are waves in the electromagnetic spectrum all the same speed?

A sound wave is much slower than a gamma wave, But the only difference is their frequency/wavelength. But if a gamma wave is faster than a sound wave due to frequency/wavelength, why for example arent gamma waves faster than infrared and visible light faster than infrared?

Although sound waves and electromagnetic waves are both waves these phenomena are nothing alike. The major difference is that sound is a mechanical wave, while an electromagnetic wave (=light) is non-mechanical. Think of a mechanical wave as "many" harmonic oscillators (=springs) which are coupled. The sound disturbs the equilibrium position of the spring. It's the disturbance of the medium which constitutes the sound wave.

Without the medium a sound wave does not exist. This simple fact lies at the heart of the mechanical wave picture and it can be used to explain many facts: E.g. why the velocity of the sound differs from different media (e.g. air vs. water), or why the sound velocity different for different frequencies (dispersion). Historically, it was hard to imagine that any wave could exists which does not need a medium to propagate in. Therefore, before 1900 it was assumed that light propagates in an otherwise non-observant medium called aether. It took a great physicist (Albert Einstein) to realise that such a medium is not necessary. By realising that all experimental results point towards the non-existence of the aether, he contemplate this idea and came up with the special theory of relativity. At the heart of this theory lies the fact that light does not need a medium to propagate.

Sound waves are not in the electromagnetic spectrum. You should hence be careful about comparing the two.

Sound waves always need a medium to propagate in, and hence their speed always depends on the medium.

An EM wave (light) can also propagate in vacuo, where its speed is a constant (and it’s invariant). This is the fundamental postulate of special relativity.

When travelling in a medium, EM waves do travel at different speeds depending on their wavelength (i.e. where they sit in the spectrum) because the index of refraction depends on frequency.

EDIT

The generic formula for the speed of a sound wave $$v_s$$ is: $$v_s = \sqrt{\frac{B}{\rho}},$$ where $$B$$ is the bulk modulus and $$\rho$$ the density of the medium.

The generic formula for the speed of an EM wave is $$c_s$$: $$c_s = \frac{1}{\sqrt{\epsilon \mu}} = \frac{1}{\sqrt{\epsilon_0 \epsilon_{\mathrm{r}} \mu_0\mu_{\mathrm{r}}}} = \frac{1}{\sqrt{\epsilon_{\mathrm{r}}\mu_{\mathrm{r}}}}\cdot\frac{1}{\sqrt{\epsilon_0\mu_0}} = \frac{1}{\sqrt{\epsilon_{\mathrm{r}}\mu_{\mathrm{r}}}} c,$$ where $$c$$ is the speed of light in vacuo (constant, invariant). $$\epsilon_{\mathrm{r}}$$ ($$\mu_{\mathrm{r}}$$) is the relative permittivity (permeability) of the medium, which is equal to $$1$$ in vacuo.
$$\sqrt{\epsilon_{\mathrm{r}}\mu_{\mathrm{r}}}$$ is actually the refractive index $$n$$ of the material, so that the speed of light in a material just becomes $$c_s = c/n$$.

• whats the formula for calculating a waves speed which includes the density of the medium its traveling in? – Octavylon Jul 11 '20 at 10:24
• Which wave, sound or EM? – SuperCiocia Jul 11 '20 at 10:38
• Both, but arent they tbe same (except that if the density of the medium is 0 then the sound wave would stop)? – Octavylon Jul 11 '20 at 13:03
• @Octavylon They aren't the same. If they were the same we'd use different names. Sound waves are sound waves. Electromagnetic waves are electromagnetic waves. Comparing sound waves to electromagnetic waves is like conspiring waves in the sea with electromagnetic waves – AnOrAn Jul 11 '20 at 13:10
• Then what differes them except frequency and wavelength? and whats the formula for both in a specific medium? – Octavylon Jul 11 '20 at 13:12

The speed of a wave is determined by the medium in which it propagates. There are actually two types of 'motion' here. In the presence of a wave, the medium 'oscillates'. The pressure or Electro-Magnetic (EM) field go up and down for sound and light respectively. The speed of these oscillations (more precisely their period) is determined by the wave frequency $$\omega$$. When the wave frequency $$\omega$$ is large, then the wave moves up and down rapidly. Analogously, the wave-length $$\lambda$$ determines the spatial 'oscillations'. When $$\lambda$$ is short, then the spatial oscillation pattern is squeezed. This spatio-temporal pattern is however not directly related to the actual speed of propagation of the wave, which is given by the ratio $$v=\lambda/\omega$$ and is usually a fixed constant.

This may be easier to understand in terms of waves on a pond: Imagine a smooth water surface with a floater in the middle. When the floater is shaken, the water moves up and down at a speed that depends on how fast and strongly it is shaken. This determines the wave frequency $$\omega$$ (or equivalently wave-lengths since $$\lambda = v\omega$$, with $$v$$ fixed). At the same time, it is also possible to observe the different process of wave propagation as the disturbance moves away from the floater. There are some technicalities here, but it turns out that the speed of this propagation is given by $$v=\lambda/\omega$$ and does not depend on how fast the floater is shaken.

I would rather (somewhat boldly) say that independently of their frequency, sound waves propagate much slower than EM waves. The names 'gamma', 'Ultraviolet', 'visible', 'Infrared' or 'radio', which apply to EM waves, denote different ranges of frequencies. The analogous terms for sound waves are ultrasound, acoustic and infrasound. A gamma waves oscillates faster than a radio wave but propagates at the same speed. It is possible for some sound and EM waves to have the same frequency, but their speed (and therefore wavelengths) will be different because they do not propagate in the same medium.

This is a very simplified answer. Wave propagation can get quite complicated:

• The medium is generally affected by waves that go though it. When the waves are strong enough, then this effect can change the wave-speed. This ultimately leads to a velocity that depends on the wave frequency. This is a complicated effect that is often weak and negligible.
• Sound waves are pressure waves. Their theoretical description rely on the approximation that there is some air to propagate through. If you drive them in an extreme way, then you will affect the physical properties of the air. This can lead to shock-waves or cavitation, for example. For this reason, I would not try to drive a sound wave at the same frequency than a gamma wave. This will probably bring you to a regime where the underlying approximations break down and more complicated 'waves' emerge.