Sound Wave Speed Calculator
Solve v = f × λ for velocity, frequency, or wavelength. Supports m/s, Hz, kHz, MHz, m, cm, ft, and other units.
What is the Speed of a Sound Wave?
The speed of a sound wave describes how fast the sound vibrations travel through a medium. In physics, this is described by the fundamental wave equation, which relates velocity, frequency, and wavelength. Understanding the speed of sound is essential in acoustics, music theory, medical imaging, sonar technology, and non-destructive testing. For comprehensive wave analysis, check our Sound Waves Calculator.
Sound Wave Speed Formula
The relationship is mathematically expressed as:
$$v = f \times \lambda$$
Where:
- $v$ = Wave propagation velocity (speed of sound)
- $f$ = Frequency of the sound wave (vibrations per second)
- $\lambda$ = Wavelength (distance between consecutive crests of the wave)
This equation can be rearranged to solve for any of the variables:
- To find Wavelength: $$\lambda = \frac{v}{f}$$
- To find Frequency: $$f = \frac{v}{\lambda}$$
Speed of Sound in Common Media
The speed of sound is not a universal constant; it depends heavily on the medium's density and elastic properties (bulk modulus in fluids, Young's modulus in solids). In general, sound travels fastest in stiff solids, slower in liquids, and slowest in gases.
| Medium | Speed (m/s) | Speed (ft/s) |
|---|---|---|
| Rubber | 60 | 197 |
| Air (20 °C) | 343 | 1,125 |
| Water (25 °C) | 1,493 | 4,898 |
| Steel | 5,960 | 19,554 |
Frequently Asked Questions
How do you calculate the speed of a sound wave?
To calculate the speed of a sound wave, multiply the wave's frequency by its wavelength ($v = f \times \lambda$). For example, if a sound wave has a frequency of 440 Hz and a wavelength of 0.78 meters, its speed is $440 \times 0.78 \approx 343\text{ m/s}$.
Does the speed of sound depend on frequency?
No, in most everyday media (like air and water), the speed of sound is non-dispersive, meaning it is constant across different frequencies. When frequency increases, the wavelength decreases proportionally to maintain the same velocity.
How does temperature affect the speed of sound in air?
In gases, the speed of sound increases with temperature because gas molecules move faster at higher temperatures. An approximation for the speed of sound in dry air is $v \approx 331.3 + 0.606 \times T$, where $T$ is temperature in degrees Celsius.
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