Sound Waves Legacy Problem #11 Guided Solution
Problem*
Mr. H recently purchased a home four blocks from the busy tollway. On a typical evening, the decibel level resulting from tollway traffic is 62 dB at the location of his house. Determine the decibel level on the same evening at a house 1 block from the tollway (four times closer).
Audio Guided Solution
This is a very difficult problem you really need to know what's going on and what we have going on here is we have a Comparison of the decibel rating at a location four blocks from a busy tollway Compared to the decibel rating one block from a busy tollway The two things that are going on is that you need to understand how decibels and intensities are related Decibels being a rating of a sounds intensity and intensity simply being a measured value of the watts per meter squared At a given location and they're related by equations Which you can find on the set on the overview pages for this set the second thing that you have going on is you have the relationship between intensity and dense and distance and that is an inverse square relationship such that if you Make the distance less the distance from a sound source less you make the intensity greater and it varies According the square of the distance variation so I'm going to begin by taking the 62 decibels and converting that to an intensity because Eventually, I want to compare the intensity four blocks away the intensity one block away. So I need to get to intensity converting 62 decibels to intensity demands that you first divide by 10 to get the number of bells 6.2 you raised the 10 to that power of 6.2 and then you multiply by 1 times 10 negative 12 You end up with an intensity four blocks away that is one point five eight four nine Times ten negative six watts per meter squared Now that's the intensity four blocks away and it's related by the distance squared factor to intensity one block away So if we just assume every blocks the same distance what we're talking about one block away is an intensity That's four squared times greater So I'm going to take the one point five eight four nine times ten negative six and I'm going to multiply it by Sixteen which is four squared I end up getting two point five three five eight times ten to the negative fifth Watts per meter squared which is the intensity one block away Finally is my last step to this problem is I need to find the decibel look the decibel rating at this location So I have to convert this number two point five three five eight times ten negative fifth Two decibels and doing so demands that I first divide by one times ten negative twelve Then once I do that I need to take the log of that number and then I need to multiply by ten And I get seventy four point oh four one decibels, and I'm just gonna round that to seventy four decibels
Solution
74 dB
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.