Speed of Sound
Calculator and formulas for the speed of sound at a given temperature
Speed of Sound Calculator
Temperature-dependent sound propagation
Calculates the speed of sound (c) in air based on temperature. The speed of sound increases with higher temperature due to faster molecular motion.
Example Calculation
Example: Speed of sound at room temperature
Problem:
How fast does sound propagate at room temperature of 20°C? Calculate the speed of sound in m/s and km/h.
Given:
- Temperature T = 20°C
- Find: Speed of sound c in m/s and km/h
Solution:
1. Speed of sound in m/s:
2. Conversion to km/h:
Temperature dependency
Physical background
Why does the speed of sound increase with temperature? At higher temperatures, air molecules move faster and can transmit vibrations more efficiently.
Formulas for speed of sound
The speed of sound in air depends mainly on temperature. At higher temperatures, air molecules move faster, allowing sound waves to propagate more efficiently.
Speed of sound in air
Calculation of speed of sound at given temperature in °C.
T = Temperature [°C]
Valid for dry air at normal pressure
Conversion m/s ↔ km/h
Conversion between different speed units.
Temperature from altitude
Approximation formula for air temperature at different altitudes.
Valid up to about 11 km altitude (troposphere)
General wave equation
Basic relationship between frequency, wavelength and speed.
Speed of sound in different media
Air (0°C): 331 m/s
Steel: ≈ 5000 m/s
Wood: ≈ 4000 m/s
Aluminum: ≈ 6400 m/s
Detailed description of speed of sound
Physical Fundamentals
The speed of sound describes how fast sound waves propagate through a medium. In gases like air, it depends mainly on temperature, as warmer molecules move faster and can transmit vibrations more efficiently.
The formula c = 331.3 + 0.606 × T is an empirical approximation for dry air at normal pressure and is valid in the temperature range from about -40°C to +40°C.
Usage Instructions
Enter the air temperature and select the unit (Celsius or Fahrenheit). The calculator automatically computes the speed of sound in m/s and km/h.
Application Areas
Acoustics and Audio Technology
Runtime calculations, room acoustics, loudspeaker design. Foundation for time-critical audio applications.
Measurement Technology
Ultrasonic measurements, sonar, distance measurement. Material testing and non-destructive testing methods.
Meteorology
Weather radar systems, atmospheric measurements. Temperature determination from speed of sound measurements.
Understanding sound propagation
Sound propagates through pressure fluctuations that are transmitted from molecule to molecule. The speed depends on the properties of the medium:
Temperature effect
+1°C ≈ +0.6 m/s
Higher temperature = faster molecules
= more efficient transmission
Medium dependency
Solids > Liquids > Gases
Density and elasticity determine
propagation speed
Practical significance
Echo runtime: t = 2s/c
Thunder: distance = t × 343 m
(at 20°C in meters)
Memory aid: At 20°C, sound travels about 343 m in one second. That's about the distance of 3 football fields!
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