Acoustic Wavelength & Sound Velocity
Relates the physical spatial wavelength lambda of a sound wave to its temporal frequency f based on ambient air temperature-dependent speed of sound c.
\[ \lambda = \frac{c}{f} \quad \text{where } c = 331.3 \cdot \sqrt{1 + \frac{T_{^{\circ}\text{C}}}{273.15}} \approx 331.3 + 0.606 \cdot T_{^{\circ}\text{C}} \]
Plain Text Formula:
lambda = c / f where c = 331.3 * sqrt(1 + T_C / 273.15) ≈ 331.3 + 0.606 * T_C
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ \lambda \] | Acoustic Wavelength | meters (m) | Peak-to-peak physical distance between sound pressure fronts |
| \[ c \] | Speed of Sound in Air | m/s | Speed of acoustic propagation (343.2 m/s at 20°C) |
| \[ f \] | Sound Frequency | Hertz (Hz) | Oscillations per second |
| \[ T_{^{\circ} ext{C}} \] | Air Temperature | °C | Ambient dry bulb temperature |
💡 Worked Engineering Example
Problem Statement:
Find the wavelength of a 100 Hz bass note in a 20°C recording studio (c = 343.2 m/s).
Step-by-Step Solution:
- lambda = c / f = 343.2 / 100 = 3.432 meters
🎯 Result: The physical wavelength of the 100 Hz wave is 3.43 meters (approx. 11.26 feet).