Pump Up the volume or Knock, Knock Knockin on Your skull wall!

February 18, 2013

Well, little Mathpiggies, lots of students want to be Sound Engineers. It is time to tell cool middle school students that Sound Engineers NEED maths.

olden days sound guy

According to Salford Uni’s Guide to Decibels:

Just about every piece of audio equipment (microphones, loudspeakers, sound cards, amplifiers, mixers, etc) will have specifications expressed logarithmically (i.e. in dBs).

We don’t want to frighten junior sound engineers with complicated formulae. But we can have a little peak at SOUND ENGINEERING.

Here’s the deal.

You want to be a Sound Engineer like this:

sound engineer 1……………………………………………………………….

Not like this:

Sound engineer 2

Sound is tricky. It is a wave of compressed air travelling through the air to your ear.

It is measured in INTENSITY (Air Pressure per sq m) or Power (eg. Energy carried per sec in, say, Kilowatts).


If you have ever been to a Rock Concert you can feel the pressure of the sound wave of the BASS hitting your chest.


Elton John

The problem, however, is your ears can detect sound pressure over an astounding range of 1 to 1 trillion. Imagine a volume Dial if we used o to a trillion:Vol dial

The other problem is your ears aren’t accurate. Your ears can detect doubling the intensity of a dripping tap but not doubling the sound of a jackhammer. This is why we can easily damage our hearing. We perceive the loudness as linear when it is not.

sound graph 1

To measure sound volume engineers use Powers or Exponents:

Start with 1 million:

1000000 = 10 x 10 x 10 x 10 x 10 x 10 = 106

we call 6 the index and 10 the base.

Similarly 100000 = 105, 10000 = 104, 1000=103, 100=102, 10=101, 1=100; so why not express numbers from 0 to 1000000 as:


We use decibels, which are 1/10 th of a Bell to measure sound.

Sound Power RAtion

But the sound intensity as measured in decibels dB is a ratio compared to the Threshold of Hearing (TOH), which is set at 100 = 1. Sometimes the sound intensity is a negative number because there are plenty of sounds below our hearing range. Just ask a dog or a bat.

Over the Threshold of Hearing

This chart is from the excellent Physics Classroom

A noise that is 3B or 30 dB louder than another noise is hitting your ear drums with 103  or 1000 times more pressure. Ahhhhhhhhhhhh!

Here is a typical sound levels chart:


Here is the ear safety chart:Ear Safety Chart

Turn Down the volume Exercise:

First, look at the chart above and compare dB readings. Note: Every 20 dB or 2 B increase in sound intensity increases the sound pressure on your ear drum by a factor of 100.

Now, we are going to convert the sound pressure in dB on the typical sound levels chart chart back from the dB (or log scale, mathpig teachers) to real scale by:

Convert to B by dividing each measurement by 10 and turning into a power and calculating value:

eg Ordinary Conversation:  60 dB = 6.0 B = 106 intensity = 1,000,000

   Rock Band: 120 dB = 12.0B = 1012 intensity = 1,000,000,000,000

If you are interested in simple explanation of volume and Guitar Amplifiers go here:

or here



  1. Dear Ms. Cue,

    I am respectfully seeking your permission to use the ear safety chart you have posted on your site. I would like to use the chart to create a handout to give to rural children when I teach hearing conservation practices. The use is entirely educational and will not be used for profit.

    Thank you,
    Kimberly Morris

    • Hello Kimberly, Ooo – Oo0! I’d be happy to give you permission but I was sent the pic via e-mail unsorced. So I cannot help you there. Good Luck. Cheerio Mathspig

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