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Wave Calculator: Frequency and Wavelength

Convert between frequency, wavelength and period for a sound wave, light or any medium, with the photon energy of light.

You can type 5e14 for visible light.

Enter the values to see the result here.

Formula

v=f λT=1fω=2πfk=2πλE=hfv = f\,\lambda \qquad T = \frac{1}{f} \qquad \omega = 2\pi f \qquad k = \frac{2\pi}{\lambda} \qquad E = h f

with speed vv in m/s, frequency ff in hertz, wavelength λ\lambda in metres, period TT in seconds and h=6.62607015×10−34h = 6.62607015\times10^{-34} J·s.

Worked example

Green light has a wavelength of 550 nm in vacuum.

  • λ=550×10−9\lambda = 550\times10^{-9} m and v=c=2.998×108v = c = 2.998\times10^{8} m/s.
  • Frequency: f=c/λ=5.45×1014f = c/\lambda = 5.45\times10^{14} Hz.
  • Period: 1/f=1.83×10−151/f = 1.83\times10^{-15} s.
  • Photon energy: hf=3.61×10−19h f = 3.61\times10^{-19} J, which is 2.252.25 eV.

Common mistakes

  • Entering nanometres or kilohertz without converting. Type 550e-9 for 550 nm and 2e3 for 2 kHz.
  • Using the speed of sound for light, or the reverse.
  • Expecting the frequency to change with the medium. Only the speed and wavelength change.
  • Confusing frequency f in hertz with angular frequency ω in radians per second.

Frequently asked questions

How are frequency and wavelength related?

Their product is the wave speed: v = f × λ. For a given medium, doubling the frequency halves the wavelength. A 440 Hz note in air has a wavelength of about 0.78 m.

Does the frequency change when a wave enters another medium?

No. The frequency is set by the source. The speed and therefore the wavelength change at the boundary, which is why sound has a longer wavelength in water than in air.

What is the energy of a photon?

E = h f, where h is Planck's constant, 6.626 × 10⁻³⁴ J·s. Green light near 550 nm carries about 2.25 electronvolts. The tool shows this when you choose light in vacuum.

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