Loudness October 18, 2006

What is it??

The Process

At the Eardrum Pressure wave arrives at the eardrum It exerts a force The drum moves so that WORK IS DONE The Sound Wave delivers ENERGY to the EARDRUM at a measurable RATE. POWER We call the RATE of Energy delivery a new quantity: POWER

POWER Example: How much energy does a 60 watt light bulb consume in 1 minute?

By the way ….. You BUY Joules from the power company.

We PAY for Kilowatt Hours We PAY for ENERGY!! Not Power/

More Stuff on Power 10 Watt INTENSITY = power/unit area 10 Watts = 10 Joules per second.

Intensity

Same energy (and power) goes through surface (1) as through surface (2) Sphere area increases with r 2 (A=4  r 2 ) Power level DECREASES with distance from the source of the sound.  Goes as (1/r 2 ) ENERGY So….

To the ear …. 50m 30 watt Area of Sphere =4  r 2 =4x3.14 x 50 x 50 = m 2 Ear Area = m 2

Continuing Scientific Notation = 2.37 x watts

Huh?? Scientific Notation = 9.5 x Move the decimal point over by 8 places. Another example: 6,326,865=6.3 x 10 6 Move decimal point to the RIGHT by 6 places. REFERENCE: See the Appendix in the Johnston Test

Scientific Notation Appendix 2 in Johnston watts = 9.5 x watts

The perception of loudness The brain is not a “linear animal”. If the ear hears a sound, it sends a certain “signal” (electrical) to the brain. The brain determines how loud the music is by the size of this signal. The range of signals in the brain is limited and it has to go over a huge range of loudness so it has to process the signal to be in a useful range. It uses something called a logarithm.

Decibels - dB The decibel (dB) is used to measure sound level, but it is also widely used in electronics, signals and communication. It is a very important topic for audiophiles. LOGARITHMIC It is a LOGARITHMIC translation so it does what the brain does.

Decibel (dB) Suppose we have two loudspeakers, the first playing a sound with power P 1, and another playing a louder version of the same sound with power P 2, but everything else (how far away, frequency) kept the same. The difference in decibels between the two is defined to be 10 log (P 2 /P 1 ) dB where the log is to base 10. ?

What the **#& is a logarithm? Bindell’s definition: Take a big number … like Round it to one digit: Count the number of zeros … 10 The log of this number is about equal to the number of zeros … 10. Actual answer is 10.3 Good enough for us!

Back to the definition of dB: The dB is proportional to the LOG 10 of a ratio of intensities. Let’s take P 1 =Threshold Level of Hearing which is watts/m 2 Take P 2 =P=The power level we are interested in. 10 log (P 2 /P 1 )

An example: The threshold of pain is 1 w/m 2

Another Example

Look at the dB Column

DAMAGE TO EAR Continuous dB Permissible Exposure Time 85 dB 8 hours 88 dB 4 hours 91 dB 2 hours 94 dB 1 hour 97 dB 30 minutes 100 dB 15 minutes 103 dB 7.5 minutes 106 dB 3.75 min (< 4min) 109 dB min (< 2min) 112 dB.9375 min (~1 min) 115 dB min (~30 sec)

Can you Hear Me???

Frequency Dependence

Why all of this stuff??? We do NOT hear loudness in a linear fashion …. we hear logarithmically Think about one person singing.  Add a second person and it gets a louder.  Add a third and the addition is not so much.  Again ….

Let’s look at an example. This is Joe the Jackhammerer. He makes a lot of noise. Assume that he makes a noise of 100 dB.

At night he goes to a party with his Jackhammering friends. All Ten of them!

Start at the beginning Remember those logarithms? Take the number =10 6 The log of this number is the number of zeros or is equal to “6”. Let’s multiply the number by 1000=10 3 New number = 10 6 x 10 3 =10 9 The exponent of these numbers is the log. The log of { A (10 6 )xB(10 3 ) } =log A + log B 96 3

Remember the definition

Continuing On The power level for a single jackhammer is watt. The POWER for 10 of them is  10 x = watts. A 10% increase in dB!