# Amplitude Of Single Tone Sound Wave = Loudness ?

• Pushless
In summary: Unfortunately, that is not the case. Instead, "loudness" is subjective and is based on the individual's perception.
Pushless
Amplitude Of Single Tone Sound Wave = "Loudness"?

Hello,

Given a single tone sound wave: x(t) = A * sin( 2 * pi * freq * t ), what does the 'A' actually represent? Peak Intensity? Intensity Level? Peak Amplitude Pressure? What is adding to my confusion is this link: http://www.jhu.edu/~signals/listen-new/listen-newindex.htm
The perceived loudness of a pure tone is proportional to a^0.6
Why a^0.6 and not 'a' and why proportional?

I am using a Matlab clone called Octave to generate wave files. These wav files contain single tone sounds. I generate the single tone with the following command:

tone1 = transpose( cPeak1 * sin( 2 * pi * fx * t ) );

I expect the variable cPeak1 to affect the "loudness" of the tone. If I increase cPeak the tone will sound louder, if I decrease cPeak it will sound softer. I have been assuming that my variable cPeak is the Intensity.

Code:
Single tone sound wave intensity: [b]I = P^2 / 2 * rho * v[/b]
I: Intensity in watts/m^2
P: Pressure amplitude in Pa

rho * v : Characteristic impedance of the air

But changing the value of cPeak does not affect the *wave* files I am generating. When I vary cPeak and plot the tones, I can see the change in amplitude. When I vary cPeak and generate wave files, the files all sound the same (in terms of loudness).

Here is a pastebin of the Octave 'm' file I am using to create the tones...I'm not sure if it will work with Matlab.

http://pastebin.com/dbKmnVwU

Thanks!

Last edited by a moderator:

In acoustics, cPeak is usually the pressure amplitude.

"Loudness" depends on how your brain interprets the signals, not on what you measure with a pressure transducer. Maybe you are not changing cPeak enough to hear the dfference, and human perception of "loudness" follows a logarithmic scale not a linear one. Try something like.

cPeak1 = floor( nMax/100 );
cPeak2 = floor( nMax/30 );
cPeak3 = floor( nMax/10 );
cPeak4 = floor( nMax/3 );
cPeak5 = floor( nMax/1 );

or even

cPeak1 = floor( nMax/10000 );
cPeak2 = floor( nMax/1000 );
cPeak3 = floor( nMax/100 );
cPeak4 = floor( nMax/10 );
cPeak5 = floor( nMax/1 );

Thank you for taking the time to read and respond to my somewhat scatterbrained OP. It was helpful. When I attempt to do/learn something new I get frustrated if I don't pick it up immediately. And once the frustration sets in, it becomes difficult for anything to sink in.

I've been reading the book "Fundamentals Of Acoustics" (Kinsler, Frey, Coppens, Sanders) in an attempt to understand the basic theory. I was getting a frustrated because the book is a little advanced. Although after reading your reply, the book was saying the exact same thing.

My issue with Octave turned out to be user error. The function that generates the audio file expects the input to be normalized.

Thank you again for your help.

If "loudness" were a simple thing to measure, there would be no complaints from TV audiences about the levels of Music vs Speech streaming to the in-boxes of all broadcasters. They would be able to get it sounding just right for every audience member.

## 1. What is the relationship between amplitude and loudness in a single tone sound wave?

The amplitude of a single tone sound wave refers to the maximum displacement of the air particles caused by the sound wave. The louder the sound, the larger the amplitude. Therefore, there is a direct relationship between amplitude and loudness in a single tone sound wave.

## 2. How is the amplitude of a single tone sound wave measured?

The amplitude of a single tone sound wave is typically measured in decibels (dB). A decibel is a unit that represents the ratio between the sound pressure level and a reference value. This reference value is usually the threshold of human hearing, which is 20 microPascals.

## 3. Can the amplitude of a single tone sound wave be changed?

Yes, the amplitude of a single tone sound wave can be changed by adjusting the energy or force behind the sound wave. For example, speaking louder or playing an instrument more forcefully can increase the amplitude and therefore the loudness of the sound wave.

## 4. Is there a limit to how high the amplitude of a single tone sound wave can be?

Yes, there is a limit to how high the amplitude of a single tone sound wave can be. This limit is determined by the physical properties of the medium through which the sound wave is traveling. If the amplitude becomes too high, the sound wave can become distorted and may even cause damage to the medium or the human ear.

## 5. How does the amplitude of a single tone sound wave affect our perception of loudness?

The amplitude of a single tone sound wave directly affects our perception of loudness. Generally, the higher the amplitude, the louder the sound will be perceived. However, our perception of loudness is also influenced by other factors such as the frequency and duration of the sound wave.

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