University of British Columbia. Physics 101 LO4

1. SOUND WAVES
L04 – Measuring Sound Levels

2. Decibels and Intensity
• The decibel is a commonly used unit for logarithmic comparisons of power or
intensity.
• It uses 10^-12 W/m^2 as a reference point (0dB). This is the quietest sound a
human can hear.
• To express the decibels of sound in terms of intensity we use:
B(I) = 0dB + 10log10(I/I0); where I0 is (0dB)
• Intensity is defined as the power transferred per unit area.
• Sound waves travel isotropically in all directions. Therefore we use the area of a
sphere when talking about sound intensity.
• To express intensity we use;
I = P/(4πr^2)

3. Question
You are a photographer for National Geographic and are trying to rare images of
the endangered Siberian Tiger in it’s natural habitat. You are aware that the
quietest sound they are capable of hearing is 10db, which is the sound intensity of
your nervous breathing. How close can you get before the tiger hears you?
Assume the tiger is asleep and cannot and notice you with it’s powerful sense of
smell
Hint: The power your breathing generates is 3x10^-8 W

4. Solution
• We know that the sound of your breathing is around 10dB. With this information you can
manipulate the equation; B(I) = 0dB + 10log10(I/I0) to calculate the intensity.
• 10dB = 0dB + 10log10(I/10^-12).
• We work out that Intensity is 1x10^-12 W/m^2
• We understand that sound waves are able to propagate isotropically with a certain radius.
This radius is what we’re looking for and it can be calculated with the equation; I = P/(4πr^2)
• The question tells you that the power generated from your breathing is 2.827x10^-8. With
this we can calculate the radius within which the Tiger can hear you
• 1x10^-12 W/m^2 = (2.827x10^-8)/ (4πr^2)
• We are then able to work out that you can get within a radius of approximately 15m of the
Tiger, without being heard.