Sound intensity level, decibels

In summary, the conversation discusses how a student typing in a computer cluster generates a sound level of 55 dB and the calculation for the dB level when there are 30 equally noisy students working in the cluster. The calculation results in a total of 31 individuals and a sound level of 69.91 dB, but the answer given is 63.8 dB. The discrepancy may be due to rounding or a different method of calculation. Further confirmation is needed to determine the accuracy of the thought process.
  • #1
jehan4141
91
0
A student typing in a computer cluster generates a sound level of 55 dB. What will the dB level the night before essays are due when there are 30 equally noisy students working in the cluster?

dBo = 55
Ihearing = 1E-12 W/m2

Bo = 10log(I/Ihearing)
55 = 10log(I/Ihearing)
55 = 10log(I/1.0E-12)
I = 3.16227766E-7 W/m2

If there are 30 other individuals, this makes a total of 31 individuals.

Itotal = 31 x I = 31 x 3.16227766E-7
Itotal = 9.80E-6 W/m2
Btotal = 10log(Itotal/Ihearing) = 10log(9.80E-6/1E-12)
Btotal = 69.91 dB ?

The answer says that it is 63.8 dB. Please can somebody help me find where in my logic I have failed? Thank you so very much everyone!
 
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  • #2
looks like a matter of significant figures to me. You are being more numerically accurate than the book. Try rounding your answers to only two or three significant figures and see how it compares.
 
  • #3
It is definitely not a matter of significant figures. Even when I tried your suggestion I still get very close to my original answer. Can anybody else please confirm if this thought process is at least correct? Thank you again.
 

Related to Sound intensity level, decibels

What is sound intensity level?

Sound intensity level, also known as sound pressure level, is a measure of the loudness of sound. It is measured in decibels (dB) and is a logarithmic scale based on the human perception of sound.

How is sound intensity level measured?

Sound intensity level is measured using a sound level meter, which detects and measures the pressure of sound waves in a given area. The meter displays the measurement in decibels and is typically calibrated to measure sound levels from 0 dB (threshold of hearing) to 120 dB (threshold of pain).

What is the relationship between sound intensity level and sound pressure level?

Sound intensity level and sound pressure level are closely related and are often used interchangeably. Sound intensity level is directly proportional to sound pressure level, which means that as sound pressure level increases, so does sound intensity level.

What is the difference between sound intensity level and sound power level?

Sound intensity level and sound power level are both measures of sound, but they differ in what they measure. Sound intensity level measures the loudness of sound at a specific location, while sound power level measures the total amount of sound energy emitted by a source.

How does sound intensity level affect human hearing?

Exposure to high levels of sound intensity can lead to temporary or permanent hearing loss, depending on the duration and intensity of the exposure. It is important to protect our ears from loud noises, as even short bursts of high-intensity sound can cause damage to our hearing.

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