1
$\begingroup$

The mathematical relation between intensity and loudness is:

$$ I_{L} = 10 \log_{10}\left( \frac{I}{I_{0}} \right) $$

where $I$ is the sound intensity and $I_{0}$ the reference intensity. The unit of sound intensity is expressed in decibels (dB).

The mathematical relation between intensity and frequency is:

$$ I = 2 \pi^{2} \nu^{2} \delta^{2} \rho c$$

with $I$ the sound intensity, $\nu$ the frequency of sound, $\delta$ the amplitude of the sound wave, $\rho$ the density of the medium in which sound is travelling and $c$ the speed of sound.

This indicates that as frequency increases, loudness must also increase.

Then, why most physics textbooks mention that Loudness does not depend on Frequency?

$\endgroup$
2
  • 2
    $\begingroup$ . . . . . why most physics textbooks mention that Loudness does not depend on Frequency? Please give an example from a Physics textbook because as it stands it is not a correct statement. $\endgroup$
    – Farcher
    Feb 20, 2023 at 14:48
  • 1
    $\begingroup$ Your second equation calculates sound intensity, typically in $W/m^2$. "Loudness" is a subjective human experience, as the sensitivity of the human ear to a given sound intensity is highly dependent on frequency. $\endgroup$ Feb 20, 2023 at 21:00

1 Answer 1

1
$\begingroup$

Personally, I am not sure where exactly you found that loudness is not frequency dependent. Loudness is a psychoacoustic quantity (measure) and according to the well known Fletcher-Munson curves (Equal Loudness Contours) there is strong frequency dependence on loudness.

You may be referring to the Sound Intensity Level (SIL), which is calculated with the first equation you provided. There seems to be a rough rule of thumb being used in the acoustics community relating Sound Intensity Level with loudness, which states that there is "roughly" doubling of loudness for a $10 ~ dB_{SIL}$ increase.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.