Calculating Sound Level Increase in a Work Environment: A Machinist's Dilemma

[tmkgemini]

The graph shows the US Department of Labor noise regulation for working without ear protection. A machinist is in an environment where the ambient sound level is of 85dB, i.e., corresponding to the 8 Hours/day noise level. The machinist likes to listen to music, and plays a Boom Box at an average level of 84.0dB. Calculate the INCREASE in the sound level from the ambient work environment level (in dB).


You don't really need the graph for this part of the problem... I have no idea how to solve this... i have the hint :Compute the intensities from the levels, add them to get the total intensity, then find the total sound level. Note the question asks for the increase... but it's still not helping. PLease help!

 

[Andrew Mason]

The graph shows the US Department of Labor noise regulation for working without ear protection. A machinist is in an environment where the ambient sound level is of 85dB, i.e., corresponding to the 8 Hours/day noise level. The machinist likes to listen to music, and plays a Boom Box at an average level of 84.0dB. Calculate the INCREASE in the sound level from the ambient work environment level (in dB).


You don't really need the graph for this part of the problem... I have no idea how to solve this... i have the hint :Compute the intensities from the levels, add them to get the total intensity, then find the total sound level. Note the question asks for the increase... but it's still not helping. PLease help!

Since difference in loudness in decibels between sounds A and B is 10log(I_A/I_B), a sound A that is x db louder than sound B has an intensity (Power/Area) of 10^(x/10) times the intensity of B. If you add these two sounds together you get a combined intensity or Power/Area of I_A + I_B. So the new loudness in decibels increases by 10log((I_A + I_B)/I_B). There will only be a few db difference by combining the two sounds.

AM

 

[wais]

To calculate the increase in sound level, we first need to convert the decibel (dB) measurements to sound intensities. This can be done using the formula I = 10^(dB/10), where I is the sound intensity and dB is the decibel level.

For the ambient sound level of 85dB, the intensity would be I = 10^(85/10) = 10^8.5 = 316,227,766.02. For the Boom Box sound level of 84.0dB, the intensity would be I = 10^(84/10) = 10^8.4 = 251,188,643.15.

To find the total intensity, we add these two intensities together: 316,227,766.02 + 251,188,643.15 = 567,416,409.17.

To convert this back to a decibel level, we use the formula dB = 10log(I/10^-12), where I is the intensity and 10^-12 is the reference intensity. Plugging in the total intensity, we get dB = 10log(567,416,409.17/10^-12) = 10log(5.6741640917 × 10^22) = 112.75dB.

Therefore, the increase in sound level from the ambient work environment level of 85dB to the level with the Boom Box playing at 84.0dB is approximately 27.75dB. This is well above the recommended noise level for a full 8-hour work day, and the machinist should consider using ear protection to protect their hearing.