Understanding the Relationship
* Speed of Sound: The speed of sound in air at standard temperature and pressure (STP) is approximately 343 meters per second (m/s).
* Frequency: The frequency of middle C is 262 Hz (Hertz), meaning the sound wave vibrates 262 times per second.
* Wavelength: The wavelength is the distance between two consecutive peaks (or troughs) of the sound wave.
The Formula
The relationship between speed, frequency, and wavelength is:
* Speed (v) = Frequency (f) × Wavelength (λ)
Calculation
1. Rearrange the formula to solve for wavelength:
λ = v / f
2. Plug in the values:
λ = 343 m/s / 262 Hz
3. Calculate:
λ ≈ 1.31 meters
Therefore, the wavelength of middle C on a piano as it travels through air at standard temperature and pressure is approximately 1.31 meters.
