The diameter of a speaker is indeed an important factor in determining its ability to reproduce different frequencies of sound. However, the relationship between speaker diameter and frequency is not solely based on the depth of travel of the speaker's diaphragm. Instead, it is influenced by a combination of factors, including the wavelength of the sound waves and the acoustic impedance of the medium.
To understand the relationship between speaker diameter and frequency, let's consider the following:
Wavelength: The wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase with each other. In general, higher frequencies have shorter wavelengths, while lower frequencies have longer wavelengths. To effectively reproduce a particular frequency, the speaker needs to move in a manner that matches the wavelength of that frequency. This means that the diameter of the speaker's diaphragm should be comparable to or larger than the wavelength of the sound it aims to reproduce. If the diaphragm is too small relative to the wavelength, it may not be able to move enough air to generate the desired sound efficiently.
Acoustic Impedance: Acoustic impedance is a property that describes how easily sound waves propagate through a medium. It depends on the density and compressibility of the medium. In the case of a speaker, the medium is usually air. A larger speaker diaphragm has a higher surface area and can interact with a larger volume of air. This increased interaction helps match the acoustic impedance of the speaker to that of the air, allowing for better transmission of sound energy across a range of frequencies.
While the depth of travel of a speaker's diaphragm does play a role in reproducing sound, it is not the sole determining factor. The diameter of the diaphragm influences the amount of air that can be displaced, the efficiency of sound generation, and the interaction with the medium. These factors collectively contribute to the ability of the speaker to reproduce different frequencies accurately. By selecting an appropriate diameter for the speaker, taking into account the wavelengths and acoustic impedance of the desired frequencies, manufacturers can optimize its performance across a wide range of sound frequencies.