Waves & Sound Calculator — Frequency, Wavelength, Doppler

Compute wavelength, frequency, period, Doppler shift and standing waves.

About this calculator

A waves and sound calculator solves problems involving wave speed, frequency, wavelength, Doppler effect, sound intensity (decibels), and resonance frequencies of strings and air columns. These cover the wave physics problems in acoustics, music theory, ultrasound imaging, and basic seismology.

The wave equation v = fλ links speed, frequency, and wavelength for every type of wave — sound, water waves, light, radio waves. The Doppler effect describes the apparent frequency shift when source and observer move relative to each other.

Formula

v = f\lambda \;;\; L_{dB} = 10 \log_{10}\left(\frac{I}{I_0}\right)

  • v — Wave speed (343 m/s in air at 20 °C)
  • f — Frequency (Hz)
  • λ — Wavelength (m)
  • I — Sound intensity
  • I₀ — Reference 10⁻¹² W/m² (threshold of hearing)

Worked example

Inputs: Wavelength of an A4 musical note (440 Hz) in air

  1. v = 343 m/s (air at 20 °C)
  2. λ = v / f = 343 / 440 = 0.78 m = 78 cm
  3. A guitar string vibrating at 440 Hz has a fundamental wavelength of 2 × string length
  4. For a 33 cm guitar string: wave speed on string = 440 × 0.66 = 290 m/s

Frequently asked questions

Why do sounds get higher pitch as the source moves toward you?

The Doppler effect: each successive wave is emitted from a position slightly closer to you, compressing the wavefronts and reducing wavelength. The observed frequency = f × v/(v − v_source). A 500 Hz siren on an ambulance moving toward you at 30 m/s sounds at 500 × 343/(343 − 30) = 548 Hz; receding it drops to 460 Hz.

Why is the decibel scale logarithmic?

Human hearing perceives loudness logarithmically — doubling the intensity (10× the pressure amplitude) feels roughly twice as loud, not 10× as loud. The dB scale matches this perception: 0 dB = threshold of hearing, +10 dB = perceived "twice as loud" (10× intensity), normal conversation 60 dB, jet engine 130 dB (threshold of pain). 60 dB is 1 million times more intense than 0 dB.

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