Sound Wave Calculator

Calculate wavelength, frequency, speed of sound, period, and distance traveled for sound waves in various media and temperatures.

Sound Wave Formulas: Wave Equation: λ = v / f v = λ × f f = v / λ Where: • λ (lambda) = wavelength (meters) • v = speed of sound (m/s) • f = frequency (hertz, Hz) Period: T = 1 / f f = 1 / T Angular Frequency: ω = 2πf (radians/second) Speed of Sound in Air: v = 331.3 + (0.606 × T) m/s where T = temperature in °C At 20°C (68°F): v ≈ 343 m/s At 0°C (32°F): v ≈ 331 m/s Distance Traveled: d = v × t Speed in Different Media: • Air (20°C): 343 m/s • Water (25°C): 1,480 m/s • Seawater: 1,500 m/s • Steel: 5,960 m/s • Aluminum: 6,320 m/s • Concrete: 3,200 m/s • Wood: 3,300-5,000 m/s Audible Range: • Human: 20 Hz - 20,000 Hz • Infrasound: < 20 Hz • Ultrasound: > 20,000 Hz Musical Notes (Equal Temperament): A4 = 440 Hz (concert pitch) Each octave doubles/halves frequency Each semitone: f × 2^(1/12) Doppler Effect: f' = f × (v ± v_observer) / (v ∓ v_source) + for approaching, - for receding
Example 1 (Wavelength of Middle C): Frequency = 261.6 Hz (C4), v = 343 m/s λ = 343 / 261.6 = 1.31 m = 131 cm Period = 1/261.6 = 3.82 ms Example 2 (Wavelength of High Pitch): Frequency = 10,000 Hz (10 kHz), v = 343 m/s λ = 343 / 10,000 = 0.0343 m = 3.43 cm (Small enough to reflect off small objects) Example 3 (Bass Frequency): Frequency = 50 Hz (low bass), v = 343 m/s λ = 343 / 50 = 6.86 m (Longer than most rooms, causes standing waves) Example 4 (Speed at Different Temperature): Temperature = 30°C (hot day) v = 331.3 + (0.606 × 30) v = 331.3 + 18.18 = 349.5 m/s Example 5 (Ultrasound Medical Imaging): Frequency = 5 MHz = 5,000,000 Hz In tissue (v ≈ 1,540 m/s): λ = 1,540 / 5,000,000 = 0.000308 m = 0.308 mm (Sub-millimeter resolution) Example 6 (Thunder Distance): Time between flash and sound = 6 seconds Distance = 343 × 6 = 2,058 m ≈ 2 km (Or: 6 / 3 = 2 km rule of thumb) Example 7 (Echo in Canyon): Round-trip time = 4 seconds, v = 343 m/s Total distance = 343 × 4 = 1,372 m One-way distance = 1,372 / 2 = 686 m Example 8 (Frequency from Wavelength): Measured wavelength = 0.5 m, v = 343 m/s f = 343 / 0.5 = 686 Hz (Between E5 and F5 musically) Example 9 (Organ Pipe Fundamental): Open pipe length L = 2 m Fundamental: λ = 2L = 4 m f = 343 / 4 = 85.75 Hz (low F2) Example 10 (Doppler - Approaching Train): Train horn: 500 Hz, train speed: 30 m/s v = 343 m/s, observer stationary f' = 500 × 343/(343-30) f' = 500 × 343/313 = 548 Hz (48 Hz higher, about 1.7 semitones) Example 11 (Room Resonance): Room dimension = 5 m First resonance: λ = 2 × 5 = 10 m f = 343 / 10 = 34.3 Hz (very low bass) Harmonics at 68.6 Hz, 102.9 Hz, etc. Example 12 (Sound in Water): Frequency = 1,000 Hz, v_water = 1,480 m/s λ = 1,480 / 1,000 = 1.48 m (Much longer than in air: 0.343 m)

What is the speed of sound?

The speed of sound in air at 20°C (68°F) is approximately 343 m/s (1,125 ft/s or 767 mph). It varies with temperature: increases about 0.6 m/s per °C. In water: ~1,480 m/s. In steel: ~5,960 m/s. Sound travels faster in denser media and at higher temperatures.

How do you calculate wavelength from frequency?

Wavelength λ = v/f, where v is sound speed and f is frequency. For example, middle A (440 Hz) at 343 m/s: λ = 343/440 = 0.78 m = 78 cm. Low frequencies have longer wavelengths; high frequencies have shorter wavelengths.

How does temperature affect sound speed?

Sound speed in air: v = 331.3 + (0.606 × T) m/s, where T is temperature in °C. At 0°C: 331 m/s. At 20°C: 343 m/s. At 30°C: 349 m/s. Higher temperature means faster molecular motion, transmitting sound faster. Humidity also affects speed slightly.

What is the audible frequency range?

Humans typically hear 20 Hz to 20,000 Hz (20 kHz). Below 20 Hz is infrasound (felt more than heard, like earthquakes). Above 20 kHz is ultrasound (used in medical imaging, dog whistles). Age reduces upper limit; many adults hear only up to 15 kHz.

How do you calculate the period of a sound wave?

Period T = 1/f, the time for one complete cycle. For 1000 Hz: T = 1/1000 = 0.001 s = 1 ms. Angular frequency ω = 2πf gives radians per second. Period and frequency are reciprocals; high frequency means short period.

What determines the pitch of a sound?

Frequency determines pitch. Higher frequency = higher pitch. Musical note A4 = 440 Hz (orchestra tuning). Each octave doubles frequency: A5 = 880 Hz, A3 = 220 Hz. Human voice: male ~85-180 Hz, female ~165-255 Hz. Pitch perception is logarithmic, matching musical scales.

How far does sound travel in one second?

At 20°C in air: 343 meters (1,125 feet). This creates a 3-second rule for lightning: count seconds between flash and thunder, divide by 3 to get distance in km (or divide by 5 for miles). Sound is much slower than light (300,000 km/s).

What is acoustic impedance?

Acoustic impedance Z = ρv (density × sound speed) measures resistance to sound propagation. Air: ~415 Pa·s/m. Water: ~1.48 million Pa·s/m. Large impedance mismatch causes reflection (why underwater sounds don't transmit well to air). Matching impedance improves transmission.

How do wavelength and room acoustics relate?

Low frequencies (long wavelengths) diffract around obstacles and create standing waves in rooms. 100 Hz has λ = 3.43 m, larger than most furniture. 10 kHz has λ = 3.43 cm, reflects off small objects. Room dimensions equal to λ/2 cause resonances. Bass traps target long wavelengths.

What is the Doppler effect for sound?

Moving sources/observers shift frequency. Approaching: f' = f(v+v_o)/(v-v_s). Receding: f' = f(v-v_o)/(v+v_s), where v = sound speed, v_o = observer speed, v_s = source speed. Examples: rising pitch of approaching siren, sonic booms when source exceeds sound speed.

How do you measure sound wavelength experimentally?

Use interference: create standing waves, measure distance between nodes (λ/2) or antinodes. Or use known frequency and measured sound speed: λ = v/f. Ultrasonic rulers measure distance by timing echoes. Resonant tubes (organ pipes) resonate at wavelengths related to tube length.

What are harmonics and overtones?

Fundamental frequency f₀ is lowest frequency. Harmonics are integer multiples: 2f₀, 3f₀, 4f₀... (overtones). Musical instruments produce complex tones with many harmonics. String length determines fundamental: f = v/(2L) for fixed ends. Timbre (sound quality) depends on harmonic content and amplitude.

🧮
Frequency Calculator
🧮
Wavelength Calculator
🧮
Decibel Calculator
🧮
Doppler Effect Calculator