How Wave Speed Works: v = f times lambda

Quick Answer

A wave's speed, or wave velocity, is how fast its crests travel, and it equals the frequency multiplied by the wavelength. What does v = f times lambda mean? The wave equation says speed is frequency times wavelength. Frequency is how many cycles pass a point each second, and wavelength is the distance from one crest to the next. For example, a 2 Hz wave with crests 3 metres apart moves at 6 metres per second. Amplitude, the height of the wave, changes its energy but never its speed. Open this wave simulator, drag a slider, and watch the speed update as you go.

How Wave Speed Works

The canvas draws a travelling sine wave. A row of dots marks the medium: notice that each dot only bobs straight up and down. The wave pattern sweeps to the right while the medium itself stays put, which is the heart of what a wave is. A red marker rides one crest so you can watch it advance by exactly one wavelength every cycle. For example, that is why v = f times lambda: each cycle moves the pattern forward one wavelength, and f cycles happen every second.

The Three Controls

Three sliders shape the wave, and only two of them change its speed.

• Frequency (f), in hertz: how many full cycles pass each second. Raise it and the crests race past faster; the period T = 1 / f shrinks.
• Wavelength (lambda), in metres: the distance between neighbouring crests. Stretch it and each cycle carries the pattern further, so the wave speeds up.
• Amplitude (A), in metres: the height of the crests. It sets how much energy the wave carries but has no effect on the speed.

What Actually Changes The Speed

In this simulator frequency and wavelength are independent, so changing either one changes the speed through v = f times lambda. In many real situations the medium fixes the speed instead: a sound wave in air always travels near 343 m/s, so playing a higher note raises the frequency and shortens the wavelength together, leaving the speed unchanged. For example, both stories obey the same equation; the difference is simply which quantity you are free to change and which one the medium pins down.

Worked Examples

For example, a 2 Hz travelling wave with a 3 m wavelength has a wave velocity of 2 times 3 = 6 m/s, straight from the wave equation. For example, to find the period of a wave, that same 2 Hz wave has a period of 1 / f = 0.5 s. For example, drag the wave taller in the simulator and the speed reading holds while the energy reading climbs, proving amplitude does not change speed.

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