When the amplitude of a sound wave increases, there is no direct effect on the spacing between compressions and rarefactions. The spacing between compressions and rarefactions in a sound wave is determined by the wavelength of the wave.
The wavelength of a sound wave is the distance between two consecutive points that are in phase with each other, such as two compressions or two rarefactions. It is typically represented by the Greek letter lambda (λ). The wavelength is inversely proportional to the frequency of the sound wave, which is the number of complete cycles the wave undergoes per unit of time.
The relationship between wavelength (λ), frequency (f), and the speed of sound (v) in a medium can be described by the formula:
v = λf
From this equation, it is evident that if the speed of sound in the medium remains constant, any increase in frequency (which corresponds to a higher pitch) will result in a decrease in wavelength. Conversely, a decrease in frequency (lower pitch) will lead to an increase in wavelength.
Therefore, it is the frequency, rather than the amplitude, that affects the spacing between compressions and rarefactions in a sound wave. As the amplitude of a sound wave increases, the wave becomes louder or more intense, but the distance between compressions and rarefactions remains unaffected, assuming the frequency and speed of sound remain constant.