How Does Amplitude Affect Frequency in Sound Waves?

[davenn]

I did indeed mean to talk about fixed amplitudes and changing the frequency. So since a higher frequency gives a higher max velocity to the air molecules and a higher pressure difference, can I say that a higher frequency has a higher power?

no, because you are forgetting that
1) speed of sound, regardless of freq, in a given medium is constant
2) at the higher freq, the molecules of air move back and forwards a much shorter distance due to the higher freq oscillation
3) The amplitude of sound waves is independent of their frequency. The amplitude determines the strength (volume) of the waves.

If so, does this mean that a higher frequency can be heard at longer distances than lower (since it possesses more kinetic energy)?

no that is incorrect
you still seem to be hung up on your original premise ... higher freq = higher amplitude with equates to higher power.
you have to get over that incorrect assumption

lower frequencies will travel longer distances as, in general, they will suffer less attenuation than higher frequencies.
this applies to both audio and RF frequencies ... there are natural and manmade examples of this

a natural example is the booms from volcanic eruptions ... in 1883 Krakatoa in the Sunda Strait, Indonesia erupted. The low freq booms and rumbles were heard up to 3000 km away in central Australia.
a manmade example ... ask yourself, when your neighbour is having a noisy party, what frequencies of sound do you hear from his stereo system inside your house ? they are the lower ones huh ... the thud thud of the bass guitar and the drums
Dave

 

[sophiecentaur]

ask yourself, when your neighbour is having a noisy party, what frequencies of sound do you hear from his stereo system inside your house ? they are the lower ones huh ... the thud thud of the bass guitar and the drums

It's not easy to compare situations when there are so many different factors. High and low frequency sounds are absorbed differently on the way through buildings (and in the open air) and you get transmission by diffraction of low frequencies more than high frequencies. Also, loudspeakers can couple low frequency sound directly to the building and that energy will propagate directly to the neighbours.
Our 'experiences' of sound are not good 'experimental' evidence of theory. The great thing about mathematical descriptions in Physics is that they can just show one relationship at a time. In cases like this, the arm waving can easily lead to invalid conclusions.