Example 1: A4 pitch (440 Hz) in air
- Wave speed v ≈ 343 m/s (sound in air at 20°C), frequency f = 440 Hz.
- λ = v ÷ f ≈ 343 ÷ 440 ≈ 0.78 m.
- In centimeters, λ ≈ 0.78 × 100 ≈ 78 cm—useful when thinking about room modes or speaker spacing.
science calculator
Wavelength Calculator
Convert frequency and wave speed into wavelength for sound, seismic, or other waves.
Results
- Wavelength (m)
- 0.78
- Wavelength (cm)
- 77.95
How to use this calculator
- Identify the wave speed for your medium and situation—for example, sound in air (~343 m/s at room temperature), sound in water, seismic waves, or any other wave speed.
- Enter this speed in meters per second.
- Enter the wave’s frequency in hertz (cycles per second). For musical notes or oscillators, convert from Hz if needed.
- We compute wavelength in meters as v ÷ f and convert to centimeters.
- Use the results to design experiments, place speakers, estimate room modes, or analyze wave behavior at different frequencies.
Inputs explained
- Wave speed (m/s)
- The propagation speed of the wave in the medium you care about, measured in meters per second. For example, ~343 m/s for sound in air at 20°C, higher in water or solids, or another speed you’ve measured or looked up.
- Frequency (Hz)
- The wave’s frequency in hertz, i.e., cycles per second. This could be the frequency of an audio tone, a vibration, or a repeating signal. Use scientific notation for very high or low values.
How it works
For a wave traveling with speed v and frequency f, the wavelength λ (distance between repeating features like crests) is given by λ = v ÷ f.
You enter the wave speed in meters per second (m/s) and the frequency in hertz (Hz, cycles per second).
We divide v by f to compute the wavelength in meters.
We then multiply the meter value by 100 to express wavelength in centimeters as well, which is often convenient for acoustics, lab setups, or small mechanical systems.
The key requirement is that speed and frequency refer to the same wave in the same medium and use consistent SI units.
Formula
λ = v / f, where v is wave speed (m/s) and f is frequency (Hz).
When to use it
- Acoustic calculations for room modes, musical notes, speaker placement, or microphone arrays, where wavelength affects standing waves and interference.
- Estimating seismic wavelengths in geophysics homework or simple earth science problems, given wave speeds in rock or soil.
- Mechanical and structural vibration problems where the wavelength of a flexural or longitudinal wave matters for resonance and design.
- General physics problems involving λ = v/f relationships in lab setups or conceptual questions.
Tips & cautions
- Make sure the wave speed you enter matches the medium and conditions you are actually analyzing—sound travels much faster in water or steel than in air.
- Convert speeds given in km/h or ft/s into m/s before using this tool to keep units consistent.
- Use scientific notation (for example, 1e3, 2.5e6) for very large or very small frequencies to reduce input errors.
- If you are analyzing electromagnetic waves, you can use this tool by entering the appropriate wave speed in the medium; for vacuum EM waves, use 3×10⁸ m/s or the dedicated EM converter.
- Assumes a constant wave speed; it does not model dispersion, where wave speed depends on frequency, or media where speed changes with depth or temperature.
- Requires inputs in SI units (m/s and Hz) for accurate results; mixing units without conversion will produce incorrect wavelengths.
- Computes wavelength only; it does not calculate period, phase, or amplitude—those require additional relationships.
Worked examples
Example 2: 10 Hz ocean surface wave moving 5 m/s
- Wave speed v = 5 m/s, frequency f = 10 Hz.
- λ = 5 ÷ 10 = 0.5 m.
- The wavelength is 0.5 m (50 cm) between crests in this simplified model.
Example 3: 1 kHz tone in water (~1,480 m/s)
- Wave speed v ≈ 1,480 m/s in water, frequency f = 1,000 Hz.
- λ = 1,480 ÷ 1,000 = 1.48 m.
- Sound at 1 kHz has a much longer wavelength in water than in air due to the higher wave speed.
Deep dive
Find wavelength from wave speed and frequency using λ = v/f for acoustics, vibrations, and general physics problems.
Enter wave speed in m/s and frequency in Hz to get wavelength in meters and centimeters without manual unit conversions.
Ideal for students, engineers, and hobbyists working with sound, seismic waves, or mechanical vibrations who want fast, reliable wavelength calculations.
FAQs
- Can I enter speed in km/h or mph?
- Not directly. Convert speed to meters per second first—for example, multiply km/h by (1000 ÷ 3600) or mph by 0.44704—then enter the converted value.
- Does this calculator work for electromagnetic waves?
- Yes, if you know the propagation speed in the medium. For EM waves in vacuum, use v ≈ 3×10⁸ m/s, or use the EM-specific frequency-to-wavelength converter that defaults to the speed of light.
- What if my wave speed depends on frequency?
- Some media are dispersive, meaning v depends on f. This calculator assumes a single speed value. For dispersive media, you’d need a model or data for v(f) and then apply λ = v(f)/f for each frequency.
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This wavelength calculator uses the simple relationship λ = v/f for idealized waves with constant speed in a uniform medium. It does not account for dispersion, attenuation, reflection, or complex boundary conditions and is intended for educational and preliminary analysis only. For detailed engineering or scientific work, consult more comprehensive models and domain experts.