Sound Intensity

Sound intensity

1. Sound INTENSITY AND DECIBELS

2. DEFINING INTENSITY I = The energy going through some area divided by that area and some amount of time . Note: increasing time DOES NOT increase intensity, in increases the amount of ENERGY   I = Intensity E = Energy A = Area t = Time

3. DEFINING INTENSITY (FURTHER) The rate at which energy changes over time is called POWER Therefore: I =  

4. DEFINING INTENSITY (FURTHERER) Units of Power = Watts /Units of Area = meters squared Therefore: intensity is in units of W/m 2

5. FORMULA FOR INTENSITY Sound travels in a SPHERE, and not in a circle. Formula for the surface area of a sphere is: Therefore: I =   Surface area of a sphere with radius r

6. RANGE OF HEARING (in general) Pain threshold of hearing: 1 W/m 2 Lowest sound humans can hear: 1 x 10 -12 W/m 2 These sounds are vibrating at less than a width of one molecule! Wow! Reference intensity  I o RANGE OF HEARING: 10 13 I o

7. DECIBELS The range of 10 13 I o (10,000,000,000,000) is far too large to be used efficiently We use DECIBELS as a more efficient range Decibels (dB) are units for logarithmic comparisons of intensity levels(loudness)

8. intensity level equation We want to compare a certain intensity ( I ) to the faintest sound a human can possibly hear ( I o )  this is a dimensionless number This number is in between the previous given range of (10,000,000,000,000) Since the decibel range is a logarithmic scale, we use log 10 on the given number.  

9. INTENSITY LEVEL EQUATION (more) So far: dB = log 10 ( ) Because they have been dubbed deci bels, the equation needs to multiplied by 10 ( dec - stems from the Greek root, meaning ten) Now: dB = 10log 10 [ ]  

10. Solving for intensity ( I ) dB = 10log 10 [ ] Need to get rid of the 10 on the right hand term, so: = log 10 [ ] To get rid of the log 10 on the right hand side, raise both sides to the tenth power: 10 dB/10 = [ ] To isolate for I, multiply both sides by I o : I o 10 dB/10 = I  

11. THANK YOU FOR READING! Aaron reyes phys 101 202

12. Works cited http:// hyperphysics.phy-astr.gsu.edu/hbase/sound/intens.html Physics for Scientists and Engineers: an Interactive Approach: Revised Custom Volume 1 – PHYS 101. Hawkes, Iqbal, et al. Toronto, Ontario. 2015. Page 251