One wave, one source, two materials. Choose a medium for each side of the dashed boundary and the simulator draws a single wave crossing it — the wavelength stretching or shrinking as the speed changes, while the frequency stays pinned at whatever you set. Both halves are drawn to one distance scale, so the change you see is the change the numbers report.
Wave Speed in Two Media
One wave, one source, two materials. Pick a medium for each side of the dashed boundary and watch the wavelength change as the wave crosses it — while the frequency, set once for the whole wave, stays exactly the same on both sides.
What Is the Wave Speed Simulator?
The wave speed simulator is a free interactive physics lab that runs in your browser — nothing to install and no sign-up. Pick two media, set the frequency, and watch the wavelength change while v = f x lambda holds on both sides. It reports medium 1 — Air, medium 2 — Water, speed ratio v2 / and frequency as you drag the sliders.
| Control | Range | Step |
|---|---|---|
| Frequency | 50 – 1000 Hz | 1 |
| String tension | 10 – 200 N | 1 |
How to Use the Wave Speed Simulator
Two rows of buttons run the lab. The top row sets the material on the left of the dashed line, the bottom row the material on the right, and each button carries that medium's current speed so all five stay comparable. Underneath sit two sliders. Frequency applies to the whole wave at once — there is deliberately no way to give each side its own value, because that situation cannot physically occur. String tension is the odd one out: it does nothing unless String is selected, which is why its label says so.
The readouts are where the point lands. Watch the speed ratio and the wavelength ratio printed beneath it: drag the frequency slider from end to end and those two numbers never come apart, because both are the same quantity wearing different clothes. Change a medium instead and only that side's speed and wavelength move — the other side sits still. The values behind those buttons, and why steel beats water beats air, are tabulated in wave speed in different media. To check a figure by hand rather than take the panel's word for it, the wave speed calculator rearranges the same equation for whatever you are missing.
What is being solved is one division per side: each medium fixes a speed, the shared frequency divides into it, and out comes that side's wavelength. For four of the five media the speed is looked up; for a string it is computed from the tension and the mass per unit length, which is the only place the second slider enters. One caveat: the animation is slowed heavily, or a few hundred hertz would be an unreadable blur. Both sides are slowed equally, so the ratio on screen is real even though the rate is not.
The habit worth breaking here is expecting the pitch to change when the material does. Almost everyone reaches for the frequency slider first and waits for it to jump on its own; it never does. Crests cannot accumulate at a boundary, so whatever arrives each second must leave each second, and the medium is left adjusting the only thing it can. That is the same bargain light strikes when it slows on entering glass and keeps its colour — the story told by the refractive index. If the frequency side of the equation is what you want next, start with the frequency formula.
Frequently asked questions
Why does the frequency stay the same when I change the medium?
Because the frequency is set by the source, not by the material. The wave arriving at the boundary delivers a certain number of crests every second, and the far side has to accept exactly that many — crests cannot pile up at the join or vanish into it, or the two halves would tear apart. So the medium is free to change the speed, and the wavelength has to move with it to keep v = f times lambda true. Frequency is the one quantity the boundary cannot touch, which is why the simulator gives you a single frequency slider rather than one per side.
What speed does the simulator use for steel, and why does it differ from other tables?
It uses 5960 m/s, the bulk longitudinal wave speed. Many textbook tables instead quote about 5,050 m/s, which is the speed along a thin rod. They are different because a thin rod is free to bulge sideways as the wave squeezes it, while a large block of steel is not, so the block behaves stiffer and carries the wave faster. Neither figure is wrong; they describe different geometries. The simulator says which one it is using in the fixed-values note under the sliders.
How does the tension slider change the wave speed on a string?
Through v = sqrt(T / mu), where T is the tension in newtons and mu is the mass per unit length, held fixed here at 6.0 g/m. Because the tension sits under a square root, the speed does not follow it proportionally: you have to pull four times as hard to travel twice as fast. Try it — move the slider from 25 N to 100 N and the string speed goes from about 64.5 m/s to about 129 m/s, exactly double. The slider does nothing at all unless String is selected on at least one side.
Does the on-screen animation speed show the real wave speed?
Not directly. A 256 Hz wave would cross the picture hundreds of times a second, so the animation is deliberately slowed to under one cycle per second and a caption inside the lab says so. What is preserved is the ratio: both sides are slowed by the same factor, so if steel looks four times faster than water on screen, it really is four times faster. The numbers in the panel are always the true ones — read those, and treat the animation as a picture of what is happening rather than a stopwatch.
Can wave speed ever depend on frequency?
Yes, and that effect has a name: dispersion. In a dispersive medium a high note and a low note genuinely travel at different speeds — it is why a prism spreads white light into colours, and why deep-water ripples of different sizes outrun each other. The five media in this simulator are all effectively non-dispersive over the range the sliders cover, which is why raising the frequency here shortens the wavelength and leaves the speed alone. Real dispersion is the exception rather than the rule at this level.
References & formula source
- Halliday, Resnick & Walker — Fundamentals of Physics, Chapter 16 (Waves I) on v = sqrt(T/μ), and Chapter 17 (Waves II) on the speed of sound.
- Young & Freedman — University Physics with Modern Physics, §15.4 (Speed of a Transverse Wave) and §16.2 (Speed of Sound Waves).
- CRC Handbook of Chemistry and Physics — speed of sound in air, helium and fresh water at 20 °C.
- NDT Resource Center / Kaye & Laby — longitudinal bulk wave velocity in steel, and why it differs from the thin-rod value.
- Further reading: Wavelength — Wikipedia