How to measure loudness?

[AlexKom]

Hello!

I am doing a project on how loudness and genre of music effect a peson's ability to concentrate on work. I have a problem in how to measure the loudness of music in system international... Can you help me?

Thank you!

[deleted-71495]

The SI unit commonly used for measuring something like loudness is the deciBel (dB). There are instruments that give you a reading in dB (often called dB-meters).

[EDS]

Hi AlexKom,

Just a few additional comments:

The acoustic dB that ivogougheschrich mentioned are often referred to as a measurement of the "SPL" or sound pressure level.

The unit is defined as 10 * Log_10(Prms/Pref)

where Log_10 is the base-ten logarithm, Prms is the time-averaged root mean square pressure due to the sound wave, and Pref is defined as 20 micro-pascals. The logarithmic units are chosen because it approximates the relationship between human hearing and sound wave amplitude. Pref is chosen to be roughly similar to size of the weakest sound a person can hear.

On a tangent: the name "dB" is actually generic and can also be applied to measurements of the ratio of other physical things, but it was originally introduced to describe sound. The word actually means "1/10 of one Bell" where the "Bell" is named after Alexander Graham Bell, and is a unit of sound so large that it isn't very useful. Often when people use the word "dB" alone as a unit name, they usually mean sound.

In addition to being called dB meters, meters that measure absolute sound level are sometimes called "sound level meters" or "SPL meters," depending on the context.

A new consumer grade meter will cost about upwards of $40 for the cheapest ones, and the more accuracy you want the more you'll pay. You can find them at an electronics shop (such as radioshack,) at music instrument shops that sell electronic instruments, and many places online. If you're going to buy one, make sure it comes with some indication of how accurate it is, what frequency range it covers, and what range of dB it will read. Some equipment is meant for companies who have to comply with hearing protection regulations, and they only work for very loud sounds in a narrow range of frequencies.

If buying a meter is tough, another option is to use a microphone and a computer. That will allow you to compare one sound to another sound, but to convert to absolute units you will have to borrow a calibrated meter from somewhere. If you've got a neighborhood music shop, or friends involved in music performances or any industry where people wear hearing protection, they might be able to lend you one. (There's also the ethically questionable possibility of buying a meter and then returning it to the store in a few days. I'm not going to recommend that you do it, but you wouldn't be the first.)

[AlexKom]

Thank you very much for your help!
But I have a question: As I understand, this device will measure the loudness of separate sounds in music. What can I do to measure the loudness of the whole song?

[EDS]

Hello Alex,

Sorry for the delay in getting back to you.

Most commercial meters will have a time-constant switch that makes them average over a longer period of time, but they generally only go up to a few seconds at the most.

Measuring the peak loudness in a whole song is easy enough - just keep an eye on the meter and note the highest level. (Digital meters will often do it for you.)

Measuring the average loudness is going to be more complicated.

One way to do it doesn't take any special equipment or require a computer. But, it takes some time. Basically, you randomly sample the song at several different points.

You could generate around 10 random numbers (for example, using this web site http://www.random.org/nform.html ) between 0 and the length of the song in seconds. Then play the song while looking at the time on your CD player and at the meter. When it gets to each of the random times you've listed, look at the meter and write down the value. (For reasons we can discuss if you like, using really random numbers rather than just picking numbers in your head is a good idea. Humans are notoriously bad at making up numbers that are truly random.)

From that, you can estimate the average loudness in the song, and you can also figure out the uncertainty on that average value.

One caveat - if you do this, remember that a dB is a logarithmic unit. You'll need to convert back to linear units before doing any math with them and then convert to dB again afterward. (For example, the mean value of two points, one at 100 dB and one at 90 dB is actually 97.4 dB, not 95 dB!) If it's not clear what that means, let me know.

The mean of the linear values will give you an average loudness. A measure of the uncertainty on that value (often called the "error on the mean") will be given by the standard deviation of your measured points divided by the square root of the number of points. You can find formula and explanations for the "mean" and "standard deviation" in most high school statistics textbooks and online. If you have trouble finding it, let me know.

A good way to report the numbers might be to do all your math in linear units and then convert both (mean + uncertainty) and (mean - uncertainty) to dB. You can then report the value as something like "85-88 dB," which tells your reader how accurate the measurement is.

If you want a better measurement, take even more random points.


A second method is to record it onto a computer through a microphone and then use audio software to calculate average values.

For example, the free program audacity (http://audacity.sourceforge.net/ ) will allow you to make a power spectrum of the song. That gives you the amount of power (relative to some arbitrary zero value) as a function of frequency.

How to turn something like that into a single metric for measuring "loudness" will depend on how much time you want to spend on it.

The simplest method is to pick a moderate human-speech frequency (somewhere in the 400Hz-1KHz range) and calibrate your computer only at that one frequency. Then assume that the response is flat over all the frequencies you care about. That will let you plot your power spectra in absolute units.

In reality, the response of both the meter and your computer microphone aren't exactly the same at all frequencies. Most meters have settings for "A-weighting," "C-weighting" and similar things. A-weighting artificially decreases the meter's response to very low and very high frequencies in an attempt to simulate the response of human ears. I think C-weighting is supposed to be constant over the meter's range. Try switching between them during the music and see how much difference it makes. If the change is small, then calibrating at a single frequency is probably fine. Most eletret condenser computer mics are pretty uniform over the range you care about.

Once you have a power spectrum in absolute units, you can do a couple of different things:

1 - Just display the power spectra themselves and don't try to come up with a single "loudness" number.

2 - Estimate the average loudness by eye. (Maybe let a couple different people try it to get a sense for how accurate this is.)

3 - Export the power spectrum as a text file and use something like a spreadsheet program to calculate an average. This is more accurate than #2, but takes more work.

For reasons we can discuss if you decide you want to do something like this, the right way to add the numbers in a power spectrum to get a total value is start out with linear values (rather than dB), square every number, add them together, and then take the square root of the result. Then use the formula for a logarithm to turn that into a number of dB.

If you decide you want to do that sort of thing and that very brief intro doesn't give you enough to get started, let me know. I'd be happy to fill in some details.

Good luck,
Erik

[EDS]

Sorry - made a wee mistake.

Replace "use the formula for a logarithm" with "use the formula for converting to dB" in the above.

[AlexKom]

Hello!

I am sorry I have not replied for a long time.
My parents bought me a sound level meter and I measured the sound level for each song. The problem is that i measured the sound level using only one headphone, but not two. Will it make the difference in results and what should I do.
Also I dicided to use the way, where I should find the mean between decibels. Can you explain me what should I do to convert it from logarithmic to linear value.

Thank you for your help!