I'm curious why brightness (light intensity) and loudness (sound intensity) aren't usually described using a spectrum, which typically shows frequency ranges. Are these quantities measured differently due to their nature, or is there another reason for this choice in representation?
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$\begingroup$ It sounds like you're describing an audio equalizer, which displays and adjusts the volume in a frequency-specific manner. It is pretty common for audio equipment to represent loudness in this manner. $\endgroup$– Nuclear HoagieCommented Nov 18 at 15:32
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$\begingroup$ @NuclearHoagie But Hearing range doesn't consider loudness like Electromagnetic spectrum doesn't consider brightness. $\endgroup$– M. Jones CloneCommented Nov 18 at 15:36
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1$\begingroup$ This question could use more detail. As Roger V.'s answer points out, the intensities of light and sound can be represented as either a spectrum (energy per unit frequency) or as a single number (total energy). They often are represented that way. You used the word, "usually." Are you asking why, in some cases, the simpler, more compact representation is desirable (E.g., why, for example, dimmer switches in people's homes have only a single slider/knob instead of having "full spectrum" controls? $\endgroup$– Solomon SlowCommented Nov 18 at 15:37
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$\begingroup$ @M.JonesClone Hearing range is considered over a "normal" low amplitude. If you need more fine-grained detail on hearing threshold considering both frequency and amplitude, you'd use an audiogram. The additional detail simply isn't needed for most applications, but there are certainly ways to look at it if you need to. For many applications, people just don't have any need to view or adjust the spectrum frequency-by-frequency - it's enough to simply turn the lights or the radio up or down. $\endgroup$– Nuclear HoagieCommented Nov 18 at 15:44
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2 Answers
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The problem is terminological - Brightness is a subjective characteristic of human light perception, not a physical quantity.
Light intensity is more physical term, but it may mean many different quantities.
Spectral density is the energy per unit frequency, and (under some definitions) intensity can be viewed as its integral: $$ I=\int d \omega S(\omega), $$ i.e., as an integral of the spectrum.
Mutatis mutandis same applies to acoustics.
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$\begingroup$ So how did the candela ("the unit of luminous intensity" -wiki) become not just a unit, but one of the 7 base units in SI? $\endgroup$– JEBCommented Nov 18 at 15:37
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$\begingroup$ @JEB IMHO, there is nothing fundamental about the choice of base units - many systems of units do with less than SI (e.g., CGS, Planck system.) I think the choice of SI units mostly reflects history and convenience - so that other quantities could be easily expressed: The choice of which and even how many quantities to use as base quantities is not fundamental or even unique – it is a matter of convention $\endgroup$– Roger V.Commented Nov 18 at 15:51
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They can be.
In many applications, people just want to know about or control the overall amplitude of a signal (think turning the lights or the radio up or down), and don't care to know or control the specifics about amplitudes at individual frequencies.
In applications where more fine-grained control or information is desired, it's certainly possible to represent amplitudes at specific frequencies. This is utterly common in the form of audio equalization, where the bass or treble can be adjusted independently. Your TV remote does not really need any more than 1 pair of buttons to turn the volume up or down for everyday use, but it's often still possible to adjust the EQ in the TV settings.
It's also common in astronomy, where emission spectra of stars are measured specifically with respect to particular frequencies, rather than overall brightness of the star.
