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The mathematical relation between intensity and loudness is:-

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

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:-

enter image description here$$ I = 2 \pi^{2} \nu^{2} \delta^{2} \rho c$$

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?

The mathematical relation between intensity and loudness is:-

enter image description here

The mathematical relation between intensity and frequency is:-

enter image description here

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

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

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?

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user355398
user355398

Confusion regarding Relation between Frequency and Loudness

The mathematical relation between intensity and loudness is:-

enter image description here

The mathematical relation between intensity and frequency is:-

enter image description here

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

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