In a sound wave, the amplitude refers to the maximum displacement or disturbance of the particles in the medium through which the sound is traveling. The relationship between the amplitude and pressure/velocity in a sound wave depends on whether we consider a longitudinal wave or a transverse wave.
In a longitudinal sound wave, the particles of the medium vibrate back and forth in the same direction as the wave propagation. When the amplitude of a sound wave increases, it means that the particles of the medium are displaced to a greater extent from their equilibrium positions. This displacement leads to variations in pressure within the medium. Therefore, an increase in the amplitude of a sound wave corresponds to an increase in the maximum pressure variation caused by the wave.
Mathematically, in a longitudinal sound wave, the pressure variation is directly proportional to the amplitude of the wave. Thus, as the amplitude increases, the pressure variation also increases. This relationship can be described by the equation:
Pressure variation ∝ Amplitude
In a transverse sound wave, the particles of the medium vibrate perpendicular to the direction of wave propagation. However, transverse sound waves are not commonly encountered in everyday situations, as sound waves in general are primarily longitudinal in nature.
It's important to note that the relationship between amplitude and pressure/velocity in a sound wave is not linear but depends on the specific characteristics of the sound wave and the medium through which it propagates.