Does changing frequency change wave speed?

No. Wave speed is determined by the medium, not the frequency. Sound travels at ~343 m/s in air regardless of pitch. Light travels at c = 3×10⁸ m/s in vacuum regardless of colour. Changing frequency changes wavelength proportionally, keeping v = fλ constant.

What is the relationship between wavelength and energy?

For electromagnetic radiation (light, radio, X-rays), energy is inversely proportional to wavelength: E = hf = hc/λ, where h is Planck's constant. Shorter wavelength means higher frequency means higher energy — which is why UV and X-rays are more energetic (and more dangerous) than visible light.

Why does sound travel faster in water than in air?

Wave speed depends on the medium's elasticity (restoring force) and density. Water is much less compressible than air — small compressions produce large restoring forces — so sound travels faster (~1480 m/s) despite water being denser. The high stiffness outweighs the higher density.

What is the difference between transverse and longitudinal waves?

In transverse waves, the displacement is perpendicular to the direction of propagation — light waves and waves on a string are transverse. In longitudinal waves, the displacement is parallel to propagation — sound waves are longitudinal. Both obey v = fλ.

Wave Speed Calculator — Frequency, Wavelength and the Wave Equation

Every wave — sound, light, water, seismic — is described by three interdependent quantities: speed, frequency, and wavelength. Know any two and you can always calculate the third using the wave equation. This relationship underlies everything from radio communications to medical ultrasound.

Wave speed v = f·λ

4.0 m/s

Frequency f2 Hz

Wavelength λ2 m

Watch the wave move — the animation shows propagation at speed v = 4.0 m/s.

The Wave Equation

$v = f\lambda$

Symbol	Quantity	SI Unit
v	Wave speed	m/s
f	Frequency	Hz (hertz = cycles per second)
λ	Wavelength	m (metres)

Rearranging:

$f = \frac{v}{\lambda} \qquad \lambda = \frac{v}{f}$

Period and Frequency

The period T is the time for one complete oscillation:

$T = \frac{1}{f}$

Angular Frequency and Wavenumber

For mathematical descriptions of waves:

$\omega = 2\pi f \quad \text{(angular frequency, rad/s)}$ $k = \frac{2\pi}{\lambda} \quad \text{(wavenumber, rad/m)}$

The wave equation in full:

$y(x, t) = A\sin(kx - \omega t)$

Worked Examples

Worked Example

Example 1 — Speed of sound

Middle C on a piano has a frequency of 261.6 Hz. The speed of sound in air is 343 m/s. What is the wavelength of this sound wave?

$\lambda = \frac{v}{f} = \frac{343}{261.6} \approx 1.31 \text{ m}$

The wavelength of middle C is about 1.3 metres — roughly the height of a child.

Worked Example

Example 2 — FM radio wavelength

An FM radio station broadcasts at 98.5 MHz (98.5 × 10⁶ Hz). Radio waves travel at the speed of light (3 × 10⁸ m/s). What is the wavelength?

$\lambda = \frac{v}{f} = \frac{3 \times 10^8}{98.5 \times 10^6} \approx 3.05 \text{ m}$

FM radio waves have wavelengths of about 3 metres — which is why FM aerials are typically 75 cm (quarter-wave) or 150 cm (half-wave) in length.

Frequently Asked Questions

Related Concepts

Fourier Synthesis →

Build complex waveforms from sine waves — each component has its own frequency and wavelength.

Wave Packets →

Superimpose waves of nearby frequencies to create localised wave packets.

Simple Harmonic Motion →

SHM is the oscillation at each point in a wave — the building block of all wave motion.

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