# Relationship between decibel and intensity 2 Very, very different things. Watts per square metre is a measure of watts per square metres. Decibels are basically ratios, and in general usage are. The relationship between the intensity of a sound wave and its pressure amplitude The decibel level of a sound having an intensity of 10–12 W/m2 is β = 0 dB. This relationship is consistent with the fact that the sound wave is produced by The decibel level of a sound having the threshold intensity of 10−12 W/m2 is β.

Well, I'll show you why. The fact that we can hear such a soft sound, 10 to the negative 12 watts per meter squared, there's a huge range of human hearing.

This means we can hear from 10 to the negative 12 watts per square meter. This is your point zero, zero, say three, four, five, six, seven, eight, nine, 10, 11, with a one watts per square meter all the way where there's no upper limit. It just blow out your ears. But once you get to about one watt per square meter, this one will start hurting. You're not going to be happy over here. You're just going to start hurting. You'll start getting hearing losses and not good.

## Decibel Scale

So it's a huge range. This one watt per square meter is a trillion times bigger than this side. This scale is just way too big. We want to scale that's small or maybe like one to to measure loudness. We don't want to measure from one to a trillion or a trillion to one. That's what log's going to do. This is a trick for this use.

This is why I love this trick. Logarithms take really big or really small numbers and turn them into nice numbers. That's why we're going to use the logarithm. Let me show you what I mean. Logarithm, if you don't remember, here's what a logarithm does. Log base 10 of a number equals, here's what it does.

### Decibel Scale (video) | Sound | Khan Academy

I'm going to stick a number in here. What log does, log is a curious guy. Log is always asking a question. Log always wants to know, okay, if I'm log base 10, log wants to know what number would I raise 10 to in order to get this number in here.

So log looks at this number in the parentheses. This entire number here and asks what number should I raise 10 to in order to get Well, we know the answer to that. We should raise 10 to the fifth. If I raise 10 to the fifth, I'll get So if five is the number I raised 10 to getthen that's the answer to this that log base 10 of is five.

Log took a huge number,and turned it into five. Log can take huge numbers, turn them into nice numbers. The logarithm base 10 of one billion would be One billion is a big number. That's hard to deal with but log takes 10 and asks what number can I raise 10 to in order to get a billion.

I should raise 10 to the ninth because I got one, two, three, four, five, six, seven, eight, nine zeros here. I raised 10 to the ninth to get this number. So the answer to this question for the logarithm is nine. Oops, that's not nine. Nine, and that's why logarithms are good. Logarithm took this enormous number of billion and turned it into nine. So logarithms take enormous scales turn them in nine scales. That's why we like this formula which is our Decibel Scale because it takes enormous intensities and small intensities, turns them into nice intensities. Let me show you an example with this equation really quick. Let's say you're talking to your friend. Maybe you're yelling at your friend. You guys are having a heated exchange.

He's next to you. These are the sound waves coming at him. You're yelling with an intensity of, say 10 to the negative fifth. That doesn't sound like a lot but that's actually, you're pretty upset here. I want to know how many decibels is this.

How do we figure out the decibels? Well, here's what we do. We use our formula for decibels. Beta, number of decibels, equals 10 log base 10 of the intensity over always 10 to the negative 12 watts per square meter because that's the softest sound we can hear.

What do I get? So I plug this into here. I'm going to get beta equals 10 times the log base 10 of 10 to the negative fifth, because that's my intensity, divided by 10 to the negative Now these are both watts per square meter. Well, what's 10 to the negative fifth divided by 10 to the negative 12 turns out that's 10 to the seventh. I end up with 10 log of 10 to the seventh. Now I don't like logs. They freak me out but I can even do this one. Log of 10 to the seventh.

Remember what log does. It asks what number do I raise 10 to in order to get the thing in the parentheses. Well, the number I raise 10 to to get the thing in this parentheses, it's already 10 to the seventh. It's already in this form. This is about the level dynamics of the amplitudes. It's often necessary to estimate how much a sound level changes. Our ears interpret a wide range of sound amplitudes, volume or loudness as change in level and change in loudness. The decibel is a very convenient unit for measuring signal levels in electronic circuits or sound pressure levels in air. However, changes in the loudness of sounds as perceived by our ears do not conform exactly to the corresponding changes in sound pressure level.

Loudness is the quality of a sound that is the primary psychological correlation of physical strength amplitude. Loudness, a subjective feeling, is often confused with objective measures of sound pressure level SPL such as decibels.

### Logarithms and Decibels | Mathematics of the DFT

Sound level or noise level is a physical quantity measured with measuring instruments. That is not the same. We are told by psycho-acousticians that a level 10 dB greater usually means "double the loudness" or "twice as loud".

A decibel is one-tenth of a bel, which is the logarithm of the ratio of any two energy-like quantities or two field-like quantities. In the newsgroups these often misunderstood statements are explained rather less accurately. The perceived loudness of the sound depends on several factors: A typical question on the internet: Decibel levels and perceived volume change A person feels and judges sound events by exposure time, spectral composition, temporal structure, sound level, information content and subjective mental attitude.

Sometimes, even the timbre or the acoustic spectrum representing the number and relative strength of overtones is regarded as one of the parameters. However, "timbre" can only count as a parameter in a figurative sense, because it does not consist of a variable with a discrete value. 