The wavelength of sound from a static source does not change because sound waves are governed by the properties of the medium through which they propagate, such as air or any other material. When a sound is emitted from a static source, it creates a disturbance in the surrounding medium, which propagates as a series of compressions and rarefactions, forming a sound wave.
The wavelength of a sound wave is defined as the distance between two consecutive points that are in phase, meaning they are at the same stage of the wave's oscillation. In the case of a static sound source, such as a stationary loudspeaker, the sound waves it generates are emitted consistently with the same frequency and wavelength.
The frequency of a sound wave is determined by the source of the sound and remains constant as long as the source remains static. The wavelength, on the other hand, is dependent on both the frequency and the speed of sound in the medium through which it travels. In air, for example, the speed of sound is relatively constant under normal conditions.
Therefore, if the source of the sound remains static and the properties of the medium remain unchanged, the speed of sound remains constant, and consequently, the wavelength remains constant as well. In this scenario, the sound wave will propagate through the medium without any significant change in its wavelength.
It's worth noting that the perception of sound can be influenced by factors such as the Doppler effect, which occurs when there is relative motion between the source of sound and the observer. This effect causes a change in the perceived frequency of the sound, but it does not alter the actual wavelength of the sound wave itself.