Wave Calculator

Calculate wavelength, frequency, and wave speed (v = f x lambda)

Wave Calculator

v = f x wavelength

Formula
v = f x lambda

What Is a Wave?

A wave is a disturbance that transfers energy from one point to another without transferring matter. Waves can be mechanical (requiring a medium, like sound and water waves) or electromagnetic (traveling through a vacuum, like light and radio waves). All waves are described by four fundamental properties: speed, frequency, wavelength, and period.

The relationship between these properties is captured in the wave equation: v = fλ. This formula is universal — it applies to sound in air, light in glass, seismic waves in rock, and ripples in water. Understanding wave behavior is essential in acoustics, optics, radio communications, medical imaging, and earthquake engineering.

How to Use the Wave Calculator

  1. Select which two quantities you know: speed, frequency, or wavelength.
  2. Enter the known values with appropriate units (speed in m/s, frequency in Hz, wavelength in m).
  3. Click Calculate to find the missing quantity.
  4. For period: T = 1/f. Enter frequency to get period in seconds.

Formula & Explanation

v = f × λ v = wave speed (m/s) f = frequency (Hz) λ = wavelength (m) T = period (s) = 1/f Derived forms: λ = v / f f = v / λ T = λ / v

Wave speed depends on the medium, not the frequency. In air at 20°C, sound travels at ~343 m/s. Light travels at 299,792,458 m/s in vacuum (c).

Worked Examples

Sound Wave (Middle C)

Middle C on a piano has frequency f = 261.6 Hz. Sound speed in air at 20°C = 343 m/s. Wavelength = 343 / 261.6 = 1.31 m. Period = 1/261.6 = 0.00383 s (3.83 ms). The wave is about 1.3 m long — roughly the height of a piano.

FM Radio Wave

An FM radio station broadcasts at 100 MHz (10⁸ Hz). Speed of light c = 3×10⁸ m/s. Wavelength = 3×10⁸ / 10⁸ = 3 m. FM antennas are designed to be half a wavelength (1.5 m) for optimal reception.

Seismic P-Wave

A seismic P-wave travels through granite at v = 5800 m/s with frequency 1 Hz. Wavelength = 5800 / 1 = 5800 m = 5.8 km. This enormous wavelength allows P-waves to travel through the entire Earth. At 10 Hz: λ = 580 m — shorter waves reveal finer geological structures.

Frequently Asked Questions

What is the difference between transverse and longitudinal waves?▾
In transverse waves, particles oscillate perpendicular to the direction of travel (light waves, water surface waves). In longitudinal waves, particles oscillate parallel to travel (sound, P-seismic waves). Both types obey v = fλ but behave differently at boundaries and in different media.
Why does sound travel faster in solids than air?▾
Wave speed depends on the medium's stiffness and density: v = √(E/ρ). Solids are much stiffer than air, so elastic forces restore oscillating particles more quickly, increasing wave speed. Sound in steel (≈5100 m/s) is about 15× faster than in air (343 m/s).
What is the Doppler effect?▾
The Doppler effect is the change in observed frequency when source and observer move relative to each other. Approaching sources have higher apparent frequency (blue-shift for light, higher pitch for sound); receding sources have lower frequency (red-shift, lower pitch). Used in radar, medical ultrasound, and astronomy.
What is standing wave resonance?▾
When a wave reflects between boundaries, standing waves form at resonant frequencies where the boundaries are nodes or antinodes. For a string of length L fixed at both ends: f_n = n × v/(2L). This is how string instruments produce musical notes — each harmonic corresponds to an integer n.
What is wave interference?▾
When two waves meet, they superpose — their amplitudes add. Constructive interference occurs when waves are in phase (amplitudes add), creating larger waves. Destructive interference occurs when they are 180° out of phase (amplitudes cancel). Noise-cancelling headphones use destructive interference to reduce unwanted sound.