Why do high-frequency sounds have shorter wavelengths?

High-frequency sounds have shorter wavelengths because of the inverse relationship between frequency and wavelength in a wave moving at a constant speed through a medium.12

In physics, the speed of a sound wave ($S$) is determined by the medium through which it travels. This relationship is defined by the fact that the number of wavelengths passing a point per second (frequency, $f$) multiplied by the length of each wave (wavelength, $\lambda$) must equal the speed of the wave:2

$$S=f\times \lambda$$

Because the speed of sound remains relatively constant for a given medium, if the frequency increases, the wavelength must decrease proportionally to maintain that speed. Consequently, high-frequency sounds—which are perceived as having a higher pitch—necessarily consist of shorter, more frequent compressions and rarefactions compared to low-frequency sounds.12