What is the wave speed?
Pick what you know about the wave, then type the values. The wave speed calculator gives the speed in m/s, km/h, ft/s and mph, with the period, the frequency and, for a string, its lowest note.
- Wave speed
- 5 m/s
The wave speed is 5 m/s.
- Wave speed (km/h)
- 18
- Wave speed (ft/s)
- 16.4042
- Wave speed (mph)
- 11.1847
- Frequency (Hz)
- 2
- Period (s)
- 0.5
- Wavelength (m)
- 2.5
- Angular frequency (rad/s)
- 12.5664
- Wave number (rad/m)
- 2.51327
Wave speed: 5 m/s. The wave speed is 5 m/s.
How to calculate
Wave speed calculator: v = f × λ from frequency and wavelength, λ ÷ T from the period, distance ÷ time, or √(F ÷ μ) on a stretched string, with the period, frequency and string fundamental.
Example with the default inputs (From Frequency and wavelength, Frequency (f) 2 Hz, Wavelength (λ) 8.20209973753281 ft): The wave speed is 5 m/s.
Method: v = f × λ = λ ÷ T; v = distance ÷ time; on a string v = √(F_T ÷ μ), with f₁ = v ÷ 2L and λ₁ = 2L for a string of length L; T = 1 ÷ f, ω = 2πf, k = 2π ÷ λ.
- A wave of one frequency travelling at a steady speed; the string is uniform and perfectly flexible.
- For a string, the fundamental assumes both ends are fixed (nodes at each end).
Worked examples
Each example is checked against the calculator on every build.
- From Distance and time, Distance 98.43 ft, Time 6 s gives Wave speed 5 m/s, Wave speed (km/h) 18.Source: OpenStax, University Physics Volume 1, §16.1 Traveling Waves (Equation 16.1, v = λ ÷ T = λf; Examples 16.1 and 16.2), https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves (retrieved 2026-10-18), Example 16.1: v = 30.00 m ÷ 6.00 s = 5.00 m/s
- From Frequency and wavelength, Frequency (f) 2, Wavelength (λ) 2.5 gives Wave speed 5 m/s, Period (T) 0.5, Frequency (f) 2, Wavelength (λ) 2.5, Angular frequency (rad/s) 12.566371.Source: OpenStax, University Physics Volume 1, §16.1 Traveling Waves (Equation 16.1, v = λ ÷ T = λf; Examples 16.1 and 16.2), https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves (retrieved 2026-10-18), Example 16.1: T = 1 ÷ 2.00 Hz = 0.50 s and λ = vT = 2.50 m, so v = fλ = 5.00 m/s
- From Period and wavelength, Wavelength (λ) 0.08, Period (T) 4 gives Wave speed 0.02 m/s, Frequency (f) 0.25, Wave number (rad/m) 78.539816.Source: OpenStax, University Physics Volume 1, §16.1 Traveling Waves (Equation 16.1, v = λ ÷ T = λf; Examples 16.1 and 16.2), https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves (retrieved 2026-10-18), Example 16.2: λ = 8.00 cm, T = 4.00 s, v = 2.00 cm/s, f = 0.25 Hz
- From String tension, Tension (F_T) 12.68 lbf, Linear density (μ) 0.000309, Linear density unit kg/m gives Wave speed 427.229 m/s.Source: OpenStax, University Physics Volume 1, §16.3 Wave Speed on a Stretched String (Equation 16.8, v = √(F_T ÷ μ); Example 16.5), https://openstax.org/books/university-physics-volume-1/pages/16-3-wave-speed-on-a-stretched-string (retrieved 2026-10-18), Example 16.5: v = √(56.40 N ÷ 3.09 × 10⁻⁴ kg/m) = 427.23 m/s
- From String tension, Tension (F_T) 4.406 lbf, Linear density (μ) 0.006, Linear density unit kg/m, String length (L) 78.74 in gives Wave speed 57.1548 m/s, Frequency (f) 14.28869, Wavelength (λ) 4.Source: OpenStax, University Physics Volume 1, §16.6 Standing Waves and Resonance (Equations 16.15 and 16.16, λ₁ = 2L, f₁ = v ÷ 2L; Example 16.7), https://openstax.org/books/university-physics-volume-1/pages/16-6-standing-waves-and-resonance (retrieved 2026-10-18), Example 16.7: v = √(19.6 ÷ 0.006) = 57.15 m/s, λ₁ = 4.00 m, f₁ = 14.29 Hz
How it works
Pick one of four ways in:
- Frequency and wavelength: v = f × λ.
- Period and wavelength: f = 1 ÷ T, then v = f × λ = λ ÷ T.
- Distance and time: v = distance ÷ time.
- String tension: v = √(F_T ÷ μ), with F_T the tension and μ the linear density (mass per length). If you give the string length L, the string's fundamental (lowest) mode has λ₁ = 2L and f₁ = v ÷ 2L, with both ends fixed.
The page also gives the period T = 1 ÷ f, the angular frequency ω = 2π × f and the wave number k = 2π ÷ λ when it knows f and λ. The speed is shown in m/s, km/h, ft/s and mph: 1 km/h = 5/18 m/s, 1 ft/s = 0.3048 m/s and 1 mph = 0.44704 m/s, all exact.
Linear density units (exact): 1 g/m = 0.001 kg/m; 1 g/cm = 0.1 kg/m; 1 lb/ft = 0.45359237 ÷ 0.3048 kg/m; 1 lb/in = 0.45359237 ÷ 0.0254 kg/m.
Rules
- Frequency from 10⁻⁹ Hz to 10²¹ Hz; wavelength, distance from 10⁻¹⁵ m to 10¹² m; period and time from 10⁻¹⁵ s to 10¹² s.
- Tension from 10⁻⁹ N to 10⁹ N; linear density from 10⁻⁹ to 10⁶ in its unit; string length from 1 µm to 10⁶ m (optional).
- Frequency, period, wavelength, ω and k show only when the method gives them: distance and time give the speed only, and the string method gives f₁ and λ₁ only with a string length.
Output format
Every result shows to 6 significant figures. Typed values are read back as exact decimals and the arithmetic is exact, so v, f and T are rounded once at the end. A string's speed is a square root: exact when the root is exact, a 64-bit float otherwise. ω and k use π, so they are floats.
Worked examples by hand
Distance and time. A crest travels 30.00 m in 6.00 s: v = 30 ÷ 6 = 5 m/s = 18 km/h.
Frequency and wavelength. f = 2.00 Hz and λ = 2.50 m: v = 2 × 2.5 = 5 m/s; T = 1 ÷ 2 = 0.5 s; ω = 2π × 2 = 12.5664 rad/s.
Period and wavelength. λ = 8.00 cm and T = 4.00 s: f = 0.25 Hz and v = 0.25 × 0.08 = 0.02 m/s (2 cm/s); k = 2π ÷ 0.08 = 78.5398 rad/m.
A guitar string. F_T = 56.40 N and μ = 3.09 × 10⁻⁴ kg/m: v = √(56.4 ÷ 0.000309) = √182,524.27 = 427.229 m/s.
A string's fundamental. L = 2.00 m, μ = 0.006 kg/m and a 2.00 kg mass hanging from it (F_T = 2.00 × 9.8 = 19.6 N): v = √(19.6 ÷ 0.006) = 57.1548 m/s; λ₁ = 2 × 2 = 4 m; f₁ = 57.1548 ÷ 4 = 14.2887 Hz.
Other questions people ask
How do you calculate wave speed?
Multiply the frequency by the wavelength: v = f × λ. A wave of 2 Hz with a wavelength of 2.5 m travels at 2 × 2.5 = 5 m/s. If you know the period T instead of the frequency, divide: v = λ ÷ T.
What is the formula for the speed of a wave on a string?
v = √(F_T ÷ μ), with F_T the tension in newtons and μ the mass per metre of the string in kg/m. A guitar string under 56.4 N with μ = 0.000309 kg/m carries waves at √(56.4 ÷ 0.000309) = 427.2 m/s.
How do you find wave speed from distance and time?
Divide the distance a crest travels by the time it takes. A crest that moves 30 m in 6 s travels at 30 ÷ 6 = 5 m/s.
Does a higher frequency make a wave faster?
No. The speed is set by the medium (the string tension and mass, or the air). At a higher frequency the waves are shorter, so f × λ stays the same.
What is the difference between frequency and period?
The frequency f is how many waves pass a point each second, in hertz. The period T is the time for one wave, in seconds. Each is 1 divided by the other: T = 1 ÷ f.
How do you get the note a string plays from its wave speed?
A string fixed at both ends plays its lowest note when its length holds half a wavelength: λ₁ = 2L and f₁ = v ÷ 2L. A 2 m string with v = 57.15 m/s plays f₁ = 57.15 ÷ 4 = 14.29 Hz.