IB HL Sound Intensity and the dB scale

To prevent permanent hearing damage, it’s a bad idea to stand close to the speakers at a rock concert.

This looks about far enough away…

Rolling Stones in Hyde Park 2013


You’ve all seen inverse square rules like this before, here the sound Intensity in watts per square metre a distance r away from a sound of P watts is shown. Intensity is simply a measure of how much energy falls per second on a 1 metre square of surface.

Curiously, the increase in hearing sensation is proportional to the fractional increase in intensity and the ear’s response to intensity is logarithmic which can be exploited to define a scale of hearing based on the ‘bel’ or more usually, the ‘decibel’ where 10dB = 1B.

An increase of 10dB implies an increase in intensity by a factor of 10, similar to the Richter scale for measuring earthquake damage.

We can think of



We’re comparing the sound we’re listening to to the lowest perceptible intensity we can perceive with perfect hearing.

It’s phenomenally small, only 1 picowatt per square metre.


This is used in all comparative dB calculations – the threshold of hearing, which increases markedly with age. Libraries, even so-called ‘silent spaces’, are probably generating an intensity of 40dB and those close to the Stones’ concert speakers will in all probability be in pain and risking permanent damage at between 120 and 130dB.

Look at Q2 and 3 on page 694. This shows how to convert a sound intensity into dB. Q4 on page 695 reminds us that sound intensities must be added, not dB values. Try Q1-5 on page 698. Check with me if you have a problem.


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