The velocity of a periodic wave is determined by the properties of the medium it travels through, not by the wave’s own frequency or amplitude. To change a wave’s speed, you need to change the medium itself or alter a physical property of that medium, such as its density, stiffness, temperature, or depth.
This is one of the most counterintuitive facts in wave physics. Shaking a rope harder or faster changes the wave’s amplitude or frequency, but the wave still travels along the rope at the same speed. The speed is locked in by the rope’s physical characteristics. Understanding why requires looking at what actually governs wave velocity in different situations.
Why Frequency and Amplitude Don’t Change Wave Speed
The fundamental relationship for any periodic wave is: velocity equals frequency times wavelength. It’s tempting to look at that equation and think that increasing the frequency would increase the speed, but that’s not how it works. In a given medium where wave speed is constant, raising the frequency simply shrinks the wavelength by a proportional amount. The two variables adjust to keep the speed the same.
Amplitude is even more straightforward. A wave with a tall crest carries more energy than a small one, but both travel at the same speed through the same medium. Think of it this way: a loud shout and a whisper both reach you at the same time from across a room. The sound waves differ in amplitude, not speed.
Waves on a String or Rope
For a wave traveling along a string, two properties control the speed: the tension in the string and its linear density (mass per unit length). The relationship is simple. Wave speed equals the square root of tension divided by linear density.
This means you have two ways to change the wave’s velocity on a string. First, increase the tension by pulling the string tighter, and waves travel faster. The string snaps back more quickly when displaced because the restoring force is stronger. Second, use a lighter string. A thinner guitar string with less mass per meter carries waves faster than a thick, heavy one under the same tension. Conversely, a heavier string slows waves down.
This is exactly why a guitar has strings of different thicknesses. The thicker, heavier strings produce lower notes not because someone is plucking them differently, but because waves move more slowly along them, creating lower frequencies for a given string length.
Sound Waves in Air
Sound travels through air at roughly 343 meters per second at room temperature (about 20°C). The primary factor that changes this speed is temperature. Warmer air means faster-moving molecules, which transmit pressure disturbances more quickly. The speed of sound is proportional to the square root of the absolute temperature of the gas.
On a hot day at 35°C, sound travels at about 352 meters per second. On a freezing day at 0°C, it drops to around 331 meters per second. That difference is enough to affect how you perceive distant sounds outdoors.
One common misconception: air pressure does not independently change the speed of sound. If the pressure around you doubled but the temperature stayed the same, sound would travel at exactly the same speed. This is because increasing pressure also increases density by the same proportion, and the two effects cancel out. The Smithsonian National Air and Space Museum confirms this directly: the speed of sound in air depends only on temperature.
Sound Waves in Solids and Liquids
In liquids, wave speed depends on two properties: the bulk modulus (a measure of how resistant the fluid is to compression) and the density. A higher bulk modulus means the fluid is harder to compress, which makes waves travel faster. Higher density, on the other hand, slows waves down. Speed equals the square root of bulk modulus divided by density.
In solids, the same logic applies, but the relevant stiffness measure is Young’s modulus, which describes how much a material resists being stretched or compressed along one direction. Steel has a very high Young’s modulus, so sound travels through it at about 5,960 meters per second, roughly 17 times faster than through air. Rubber, which is far less stiff, carries sound much more slowly despite being a solid.
To change wave speed in these materials, you would need to change either the stiffness or the density. Heating a metal, for instance, slightly reduces its stiffness and can alter wave speed. Switching from freshwater to saltwater increases both density and bulk modulus, with the net effect being a faster speed of sound in seawater (about 1,530 meters per second versus 1,480 in fresh water).
Light and Electromagnetic Waves
Light in a vacuum always travels at 300,000 kilometers per second. Nothing changes this. But when light enters a transparent material, it slows down by an amount determined by the material’s refractive index.
The refractive index is essentially a ratio: it tells you how much slower light moves in a material compared to a vacuum. Water has a refractive index of 1.3, so light slows to about 225,000 kilometers per second. Glass (refractive index 1.5) brings it down to 200,000 kilometers per second. Diamond, with a refractive index of 2.4, slows light to just 125,000 kilometers per second, about 60% below its vacuum speed. This dramatic slowdown is part of what gives diamonds their sparkle, because the speed change causes light to bend sharply at the surface.
To change the velocity of light, you change the medium it passes through. Moving from air into water, glass, or diamond each produces a different speed. The frequency of the light stays the same during these transitions, but the wavelength shrinks in proportion to the speed reduction.
Water Waves and Depth
Ocean and lake waves follow their own rules. In shallow water, wave speed depends on the depth of the water. The relationship is straightforward: speed equals the square root of gravitational acceleration times the water depth. In deeper water, waves move faster. As waves approach a beach and the water gets shallower, they slow down. This is why waves bend (refract) as they approach a shoreline at an angle, and it’s why tsunamis, which travel across deep ocean basins, move at jetliner speeds but slow dramatically as they reach coastal shallows.
For deep-water waves where the depth is much greater than the wavelength, the speed instead depends on the wavelength itself. Longer-wavelength swells outrun shorter chop, which is why surfers see smooth, long-period swells arrive at shore well before choppy wind waves from the same distant storm.
Dispersive Media: When Frequency Does Matter
There is one important exception to the rule that frequency doesn’t affect wave speed. In what physicists call dispersive media, the wave speed actually does depend on frequency. Glass is a common example: blue light (higher frequency) travels slightly slower through glass than red light (lower frequency). This is exactly why a prism splits white light into a rainbow. Each color travels at a slightly different speed, bends by a slightly different angle, and separates out.
In dispersive media, two different velocities become important. The phase velocity describes how fast the individual wave crests move. The group velocity describes how fast the overall wave packet, and its energy, moves. These two can differ significantly. In a plasma, for instance, the phase velocity can exceed the speed of light while the group velocity stays below it. No energy or information actually moves faster than light, but the wave pattern itself can appear to.
For most everyday situations involving sound in air, waves on a string, or ripples in water, dispersion is either absent or minor, and the simple rule holds: the medium controls the speed, not the frequency.