If low and high-frequency sounds were not traveling with the same speed, it would have an impact on the wavelength of the respective sounds.
In a medium such as air or water, the speed of sound is determined by the properties of the medium itself, such as its density and elasticity. Normally, in a given medium, all sound waves would travel at the same speed, regardless of their frequency. This means that low-frequency sounds and high-frequency sounds would have the same speed and therefore the same wavelength.
However, if we consider a hypothetical scenario where low and high-frequency sounds have different speeds, it would lead to a situation where their wavelengths are no longer directly proportional to their frequencies. The wavelength of a sound wave is inversely proportional to its frequency, according to the formula:
Wavelength = Speed of Sound / Frequency
If the speeds of low and high-frequency sounds differ, their respective wavelengths would also differ. For example, if low-frequency sounds traveled slower than high-frequency sounds, low-frequency waves would have longer wavelengths compared to their frequencies, while high-frequency waves would have shorter wavelengths compared to their frequencies.
This discrepancy in wavelength could have various consequences. For instance, it might affect the propagation and interference patterns of sound waves, potentially leading to distortions or variations in how we perceive different frequencies. However, it's important to note that in reality, low and high-frequency sounds do travel at the same speed in a given medium, resulting in a consistent relationship between wavelength and frequency.