Coffee Phil wrote: ↑
15 Aug 2019 18:45
Hi H. callahan,
Sorry, I guess I thought the question was rhetorical.
OK, there are several statements there.
First I believe you are saying that if you have guitar string which is tuned to 100 Hz, then shorten it to where it is tuned to 200 Hz. To achieve the same amplitude of vibration two times the energy will have to be stored in it at 200 Hz than required at 100 Hz. To that, I don't know the answer.
From the above you conclude that by nature sound waves are constant velocity as opposed to constant amplitude. I have no idea what might be meant by constant amplitude sound waves other that sounds of the same volume. The velocity of propagation of sound is ~ 1100 ft/second at sea level and I don't think that is a strong function of frequency, so I would say sound waves have constant velocity.
How any of the above relates to how a diaphragm in an acoustic cutting head responds to sound pressure of varying frequencies so far escapes me.
Now that you kindly went into my example we finally can go on.
If i understand you correct, you also assume nature of soundwaves to be constant velocity. So, to again use the example of the acoustic guitar, a 100Hz vibration of a string having the same volume as a 200Hz vibration of a string will have double the amplitude.
Meaning though both frequencies, 100Hz and 200Hz, have the same volume, the string vibrating at 100Hz does move double the distance left and right while vibrating than the string vibrating at 200Hz.
It can´t be any other way, because vibrating at same amplitude but double the frequency should take more energy, than vibrating at lower frequency but same amplitude. But as it does not take double the force to pluck a 200Hz tone out of a guitar having the same volume like a 100Hz tone, nature of sound must be constant velocity.
So my next question, please to be answered, is:
The strings of the guitar now will set the air molecules into motion, by that the soundwave created by the guitar will spread into the room, or wherever the guitar is played.
In what way will these air molecules now be set into motion? Will they:
a: vibrate at same amplitude very frequency, assuming each frequency being played at same volume
b: vibrate at greater amplitude at low frequencies and fewer amplitude higher frequencies - assuming low and high frequencies being played at same volume
c: vibrate at lower amplitude at low frequencies and higher amplitude at high frequencies, assuming low and high frequencies being played at same volume?