Sound Wave Loudness for Finite Waves

[yetar]

I have asked this before, but I didnt get the answer I was looking for.

I was told the sound wave loudness of a wave is proportional to the amplitude^2 .
This is true to perfect waves.
However, most sound waves in nature have compact base and are not of infinity length.
Which means, what would be the average loudness or the loudness of a sound wave that does not have a certain ampiltude. Maybe somthing like:
f(X) =
|X|*sin(X) if 0<X<1
(2-|X|)*sin(X) if 1<X<2
And 0 everywhere else.

Will it be integral of |f(X)|/2 ?

Thanks in advance.

 

[LightHero]

No, the loudness of a sound wave that does not have a certain amplitude cannot be determined simply by taking the integral of |f(X)|/2. The loudness of the sound wave depends on several factors including the amplitude, frequency, and the medium through which the wave is travelling. For example, if the wave is travelling through air, then the loudness would depend on the air density and temperature.

 

[charng]

I would like to clarify that the loudness of a sound wave is not solely determined by its amplitude. While amplitude is a factor in determining loudness, it is also influenced by other factors such as frequency, distance from the source, and the sensitivity of the human ear. Additionally, the concept of "perfect waves" does not exist in nature as all sound waves are subject to interference and other environmental factors.

To accurately measure the loudness of a finite sound wave, we use a unit called decibels (dB). This unit takes into account all the aforementioned factors and provides a more accurate representation of loudness. In your example, the loudness of the sound wave would be determined by calculating the decibel level of each segment of the wave and then taking the average.

It is also worth noting that the integral of a sound wave, as in your equation, does not necessarily represent its loudness. The integral represents the total energy of the wave, which is not the same as loudness.

I hope this clarifies any confusion and provides a more thorough understanding of sound wave loudness.