The loudness of a sound wave does not directly depend on its wavelength. Loudness is primarily determined by the amplitude (or intensity) of the sound wave, which represents the amount of energy carried by the wave.
Wavelength, on the other hand, is a characteristic of the spatial pattern of the wave. It is the distance between two consecutive points in the wave that are in phase (e.g., peak to peak or trough to trough). Wavelength is inversely related to the frequency of the sound wave, meaning that longer wavelengths correspond to lower frequencies and shorter wavelengths correspond to higher frequencies.
The perception of loudness by our ears is related to the intensity of the sound wave, which is the amount of energy passing through a given area per unit of time. The greater the amplitude or intensity of a sound wave, the louder it appears to us.
However, it's important to note that the perceived loudness of a sound can also be influenced by other factors, such as the frequency content of the sound. Our ears are more sensitive to certain frequency ranges, particularly in the mid-range frequencies, around 1 kHz to 4 kHz. Therefore, even if two sound waves have the same intensity, a higher frequency sound wave within the sensitive range may appear louder to us than a lower frequency sound wave outside that range.
In summary, while the wavelength of a sound wave does not directly determine its loudness, it is an important parameter that affects the pitch or perceived frequency of the sound. Loudness, on the other hand, is primarily determined by the intensity or amplitude of the sound wave.