Sound Calculator

Speed of Sound · Frequency · Wavelength · Mach Number | Physics & Acoustics Tool

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📝 Step-by-step solution
Select what to calculate and enter values
💡 Speed v in m/s | Frequency f in Hz | Wavelength λ in meters | 1 Hz = 1 cycle/second

📖 What is Sound?

Sound is a mechanical wave that travels through a medium (air, water, solids) as a series of pressure variations. The three fundamental properties of any sound wave are:

These three are connected by the wave equation:

v = f × λ

Where:
• v = Speed of sound (m/s)
• f = Frequency (Hz)
• λ (lambda) = Wavelength (m)

🔁 Rearranged Formulas

Speed: v = f × λ
Frequency: f = v / λ
Wavelength: λ = v / f

🌡️ Speed of Sound in Air (Temperature-Dependent)

The speed of sound in dry air depends on temperature:

v = 331.3 + 0.606 × T

Where T = temperature in °C
• At 0 °C → 331.3 m/s
• At 20 °C → 343.4 m/s
• At 25 °C → 346.5 m/s

📝 Worked Example

Example 1: Finding Wavelength of a 440 Hz Tuning Fork (at 20°C)
Given: Frequency f = 440 Hz | Temperature T = 20°C

Step 1: Speed of sound = 331.3 + 0.606 × 20 = 343.4 m/s
Step 2: λ = v / f = 343.4 / 440
Result: λ ≈ 0.78 m (78 cm)

This is the standard "A4" musical note — its wavelength in air at room temperature is about 78 cm.
Example 2: Mach Number of a Jet Flying at 900 km/h
Given: Jet speed = 900 km/h | Speed of sound at altitude ≈ 300 m/s

Step 1: Convert 900 km/h to m/s: 900 × 1000 / 3600 = 250 m/s
Step 2: Mach = 250 / 300 = 0.83
Result: The jet flies at Mach 0.83 — below the speed of sound.

📊 Speed of Sound in Different Media

🚀 What is Mach Number?

The Mach number (M) is the ratio of an object's speed to the speed of sound in the surrounding medium:

M = v_object / v_sound

• M < 1 — Subsonic (slower than sound)
• M = 1 — Sonic (speed of sound)
• M > 1 — Supersonic (faster than sound)
• M > 5 — Hypersonic

🎵 Real-World Applications

⚠️ Limitations & Assumptions

📌 Important Notes
  • Speed of sound formula v = 331.3 + 0.606T is valid for dry air only. Humidity slightly increases speed.
  • Speed of sound in air is independent of pressure at a given temperature.
  • For other media (water, steel), the speed depends on elasticity and density.
  • Mach number depends on the speed of sound at that specific altitude and temperature.
  • Results are theoretical estimates assuming ideal conditions.

📚 Sources & References

Authoritative Sources

  • NIST — Speed of Sound in Dry Air
  • NASA Glenn Research Center — Mach Number & Sound Speed
  • OpenStax — University Physics, Volume 1 (Waves & Sound)
  • CRC Handbook of Chemistry and Physics
  • Khan Academy — Wave properties

❓ Frequently Asked Questions

What is the speed of sound?
The speed of sound is the distance a sound wave travels per unit time. In dry air at 20°C, it's approximately 343 m/s (1,235 km/h or 767 mph). It depends on the medium and its temperature.
Does sound travel faster in water or air?
Sound travels about 4.3 times faster in water (≈1,480 m/s) than in air (≈343 m/s), because water is much less compressible than air.
What is the wavelength of a 1000 Hz sound?
At 20°C in air (v = 343 m/s): λ = 343 / 1000 = 0.343 m (34.3 cm).
What is Mach 1?
Mach 1 is the speed of sound itself. At sea level in dry air at 15°C, that's about 1,225 km/h (761 mph or 340.3 m/s).
Why does sound travel faster in solids?
Because the particles in solids are tightly packed and strongly bonded. This means vibrations transfer more quickly from one particle to the next, resulting in higher wave speed.

🔗 Related Calculators

Physics Calculator Kinematics (SUVAT) Wavelength Calculator λ = c / f Frequency Calculator f = 1 / T Energy Calculator E = m × c² etc. Density Calculator ρ = m / V Unit Converter Speed, length, mass
⚠️ Disclaimer
This Sound Calculator is provided for informational and educational purposes only. The speed of sound formula for air assumes dry air at standard atmospheric pressure. Real-world values may vary due to humidity, altitude, pressure, and medium composition. Always verify critical calculations with authoritative physics references or a qualified professional.