Understanding the Relationship
* Frequency (f): Measured in Hertz (Hz), represents the number of waves passing a point per second.
* Wavelength (λ): The distance between two consecutive crests or troughs of a wave.
* Speed of Sound (v): The speed at which sound travels through a medium (e.g., air). This varies depending on the temperature and medium. We'll assume standard room temperature for this calculation.
The Formula
The relationship between frequency, wavelength, and the speed of sound is:
* v = fλ
Solving for Wavelength (λ)
1. Speed of Sound in Air: At room temperature (approximately 20°C), the speed of sound in air is about 343 meters per second (m/s).
2. Convert kHz to Hz: 20 kHz is equal to 20,000 Hz.
3. Rearrange the formula: λ = v / f
4. Plug in the values: λ = 343 m/s / 20,000 Hz
5. Calculate: λ = 0.01715 meters
Converting to More Convenient Units
* Centimeters: 0.01715 meters * 100 cm/meter = 1.715 cm
Therefore, the wavelength of a 20 kHz sound wave in air at room temperature is approximately 1.715 centimeters.
