Sound Waves Legacy Problem #10 Guided Solution
Problem*
According to Guinness, the record for the loudest burp is held by Paul Hunn of London. In September of 2008, his burp was measured at 107.1 dB, Determine the intensity in W/m2 of Paul's burp.
Audio Guided Solution
In this problem, we wish to convert from a decibel rating to an intensity value, taking a 107.1 dBs and finding what equivalent amount of watts per meter squared is this. To do so, we either need an equation or have to think real conceptually about how this all works. So, I'm going to begin with the equation. You can find the equation if you click the link to the overview page for this set of problems. The equation goes something like this. The intensity is equal to 1 times 10 to the negative 12 multiplied by 10 raised to a power and the power being the bell rating or the decibels divided by 10. So I need to do this in three steps beginning with finding the bell rating, 107.1 dBs is the same as 10.71 bells. Second step, I need to raise 10 to the power, the power being 10.71 bells. When I do that, I get 1 times 10 to the 10.71 power. You may have done it on your calculator and gotten a slightly different number. And then the final step, I need to take the result and multiply it by the threshold of hearing, 1 times 10 to the negative 12 watts per meter squared. When I do that, I end up getting 5.1286 times 10 to the negative second and you can round that to four significant digits. Now approaching the same problem conceptually means that you really need to understand the so-called decibel scale, which is a logarithmic scale that tells you how many times more intense one sound is in the threshold of hearing. So the idea of the logarithmic decibel scale is it's based on powers of 10. And so 10, 107.1 decibels is the same as 10.71 bells. And that tells me that this sound, the burr, is 10 raised to the 10.71 times more intense than the 1 times 10 to the negative 12 watts per meter squared, known as the threshold of hearing. So essentially, you're going to take the 10 and raise it to the power 10.71 and multiply by 1 times 10 to the negative 12 and you've got your answer. It's pretty much the same thing, but you're approaching it more based on understanding of the scale than you are upon an equation.
Solution
0.05129 W/m2
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., \(\descriptive{v}{v,velocity} = 345\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 1.28 \unit{m}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Sound Waves at The Physics Classroom Tutorial.