The frequency of a sound wave remains constant when the pressure of an ideal compressible gas increases, stays constant, or decreases, as long as the physical properties of the medium through which the sound wave propagates remain unchanged.
The frequency of a sound wave is determined by the source of the sound, such as a vibrating object or a speaker, and it does not depend on the properties of the medium it travels through (assuming the medium is linear and uniform). The frequency of a sound wave is the number of oscillations or cycles it completes in one second and is typically measured in Hertz (Hz).
When a sound wave travels through an ideal compressible gas (like air), changes in pressure will affect the wave's amplitude and wavelength, but not its frequency. Here's a brief explanation of what happens:
Increase in pressure: If the pressure of the gas increases, the sound wave will experience an increase in amplitude, which means the maximum displacement of the particles in the medium from their equilibrium position will be greater. However, the number of oscillations (frequency) per second remains the same.
Constant pressure: If the pressure of the gas remains constant, the sound wave will propagate through the medium at a constant frequency, amplitude, and wavelength.
Decrease in pressure: If the pressure of the gas decreases, the sound wave will experience a decrease in amplitude, which means the maximum displacement of the particles in the medium from their equilibrium position will be smaller. However, as with an increase in pressure, the number of oscillations (frequency) per second remains unchanged.
In summary, changes in pressure of an ideal compressible gas affect the amplitude and wavelength of a sound wave but do not alter its frequency. The frequency remains constant as it is determined solely by the source of the sound.