Sound propagation and speed

Strike a tuning fork and clap your hands over a valley, and the sound reaches you back only after a noticeable pause — long enough to count seconds on your fingers. That pause is not magic; it is the finite time sound takes to travel through air as a longitudinal mechanical wave, a chain of compressions and rarefactions passing from particle to particle. Unlike light, sound cannot leap across empty space — it needs a medium to push against, and how quickly it gets through that medium depends entirely on how tightly and elastically the medium's particles are bound to each other. This article looks at how sound propagates, why its speed varies so much across solids, liquids and gases, what else changes that speed, and why the gap between the speed of sound and the speed of light shows up so dramatically in everyday life — most famously, in the delay between seeing lightning and hearing thunder.

The core insight

Sound travels as a wave of compressions and rarefactions through a material medium, at a speed set by how closely and elastically that medium's particles are bound — fastest in solids, slowest in gases — and that speed is always many orders of magnitude smaller than the speed of light.

The core idea

Propagation as compressions and rarefactions. When a source vibrates — a tuning fork prong, a vocal cord, a drum membrane — it alternately pushes and pulls the particles of the surrounding medium. In air this creates a compression (particles crowded together, pressure momentarily higher) immediately followed by a rarefaction (particles spread apart, pressure momentarily lower). These regions travel outward from the source one after another; it is the disturbance pattern that moves, not the individual air particles, which only oscillate back and forth about their resting positions. Because each particle must physically collide with and push its neighbour, sound has no way to cross a vacuum — there is nothing there to push. Light needs no such handoff, since it is an electromagnetic wave, which is why light reaches us from the vacuum of space but sound never could.

Why solids beat liquids beat gases. The speed of sound depends on how quickly a vibration can be relayed from one particle to the next, which in turn depends on how tightly and elastically the particles are held together.

In solids, particles sit close together with strong bonds, so a push on one particle is transmitted to the next almost immediately — sound is fastest here, often several kilometres per second.
In liquids, particles are more loosely bound than in a solid but still close together, giving an intermediate speed.
In gases, particles are far apart and must travel a relatively long way before colliding with a neighbour, so the relay is slowest.

V_{\text{solid}} > V_{\text{liquid}} > V_{\text{gas}}

As typical figures: about $340\ \text{m/s}$ in air, about $1500\ \text{m/s}$ in water, and $5000\ \text{m/s}$ or more in steel — a spread of more than tenfold from gas to solid.

Other factors that change the speed. Besides the nature of the medium, two more things matter for a gas like air:

Temperature raises the speed of sound, because hotter particles move faster on their own and hand on a vibration more quickly.
Humidity raises the speed slightly, since moist air is marginally less dense than dry air for a given pressure.

Speed of sound does not depend on how loud the sound is or on its pitch — a loud low-pitched drumbeat and a faint high-pitched whistle travel through the same air at the same speed.

Figure

A bar chart comparing typical sound speed in air water and steel showing the sharp rise from gas to liquid to solid

The sound-light speed gap. Light travels at about $3\times10^{8}\ \text{m/s}$ — roughly a million times faster than sound in air. Both a lightning flash and its thunder are produced at essentially the same instant, but the flash reaches an observer's eyes almost instantly while the thunder, travelling at only $340\ \text{m/s}$ , takes several seconds to arrive. The farther the storm, the longer this gap.

Derivation AWhy the thunder-lightning delay is essentially a sound-only travel time

Given a distance $d$ between a storm and an observer, the goal is to show that the measured delay between seeing the flash and hearing the thunder can be treated, to a very good approximation, as the time sound alone takes to cover $d$ — even though light also takes a nonzero time to arrive — and to justify this by comparing the two travel times numerically for a realistic distance.

Step 1. Write the true delay as the difference between the two arrival times. Light arrives after a time $t_{\text{light}} = d/c$ and sound arrives after $t_{\text{sound}} = d/V$ , where $c = 3\times10^{8}\ \text{m/s}$ and $V \approx 340\ \text{m/s}$ is the speed of sound in air. The delay actually measured by a stopwatch, started at the flash and stopped at the thunder, is $t_{\text{delay}} = t_{\text{sound}} - t_{\text{light}} = \dfrac{d}{V} - \dfrac{d}{c}$ .

Step 2. Check the size of the light term for a realistic storm distance, say $d = 1000\ \text{m}$ . Then $t_{\text{light}} = d/c = 1000 / (3\times10^{8}) \approx 3.3\times10^{-6}\ \text{s}$ , about three microseconds — utterly unnoticeable to a person with a stopwatch or a heartbeat.

Step 3. Compare it with the sound term over the same distance: $t_{\text{sound}} = d/V = 1000/340 \approx 2.94\ \text{s}$ . The light term is about a million times smaller than the sound term (matching the million-fold speed gap between $c$ and $V$ ), so dropping it changes the delay by less than a millionth of a second.

Step 4. Conclude the working approximation used throughout this topic: $t_{\text{delay}} \approx t_{\text{sound}} = d/V$ , so the distance to a storm (or any distant sound source, given the delay) can be found from $d \approx V \times t_{\text{delay}}$ . This is exactly the distance-speed-time relation used in the worked example below, and it is valid precisely because the speed of light so vastly exceeds the speed of sound.

Worked example

A student sees a lightning flash and hears the thunder $4\ \text{s}$ later. Taking the speed of sound in air as $V = 340\ \text{m/s}$ and treating the light's travel time as negligible (as justified above), find how far away the lightning struck.

Step 1. Identify the given quantities: delay $t = 4\ \text{s}$ , speed of sound $V = 340\ \text{m/s}$ .

Step 2. Apply the approximation from the derivation: since $t_{\text{light}} \ll t_{\text{sound}}$ for any storm within ordinary sight range, the full $4\ \text{s}$ delay is treated as sound-only travel time, so $d = V \times t$ .

Step 3. Substitute the values: $d = 340 \times 4 = 1360\ \text{m}$ .

The lightning struck about 1360 m (1.36 km) away from the student.

Competitive stretch

If the same student later times a delay of $9\ \text{s}$ for a second flash, the distance scales the same way: $d = 340 \times 9 = 3060\ \text{m}$ , about $3.06\ \text{km}$ — over twice as far as the first strike, even though the delay only grew from $4\ \text{s}$ to $9\ \text{s}$ , since distance is directly proportional to the timed delay for a fixed speed of sound.

Common traps

Thinking sound can squeeze through a vacuum "if it's loud enough" — sound is a mechanical wave and absolutely needs a medium; this has nothing to do with loudness or intensity.
Assuming gases carry sound fastest because "gases are light and move freely" — the reverse is true: tightly bound, elastic solids relay vibrations fastest, and loosely packed gases relay them slowest.
Believing the lightning and thunder happen at different moments — they occur simultaneously at the source; only their arrival times differ, because light and sound travel at wildly different speeds.
Treating $340\ \text{m/s}$ as a fixed universal constant rather than a value that applies at ordinary room temperature — the speed of sound in air actually rises as temperature rises.

Ask the tutor: curious how the speed of sound is actually measured in a lab, or want more distance-speed-time problems using echoes and thunder? Ask the AI tutor for a few guided practice questions.

Why does sound travel faster in solids than in gases if solids seem so much heavier?

It is not about total mass but about how tightly and elastically neighbouring particles are bonded. In a solid, particles are locked close together by strong intermolecular forces, so a vibration passed to one particle reaches its neighbour almost instantly. In a gas, particles are far apart and must travel some distance before colliding, which slows down how quickly the disturbance is relayed. Being "heavier" per particle does not help — what matters is the speed of the particle-to-particle handoff, and tight elastic bonding wins.

If light and sound start at the same instant, why does light not also take a "delay" we notice?

Light does take time to travel — nothing outruns causality — but at $3\times10^{8}\ \text{m/s}$ it covers a kilometre in about three microseconds, far too fast for human senses or an ordinary stopwatch to register. Sound, at only $340\ \text{m/s}$ , takes roughly three seconds to cover the same kilometre. So both delays exist, but only the sound delay is large enough to notice, which is why we treat the light's travel time as effectively zero in thunderstorm problems.

Does the speed of sound change with how loud or how high-pitched the sound is?

No. Loudness depends on the amplitude of the vibration and pitch depends on its frequency, but neither changes how fast the disturbance itself travels through a given medium at a given temperature. A soft, low hum and a sharp, loud shout launched into the same air at the same moment arrive at a listener's ear after exactly the same travel time, because the speed of sound is a property of the medium, not of the particular sound being sent through it.

Sound propagation and speed

The core idea

Worked example

Competitive stretch

Common traps

Before this

Where this leads