Calculating Total Sound Intensity and Combined Sound Level: Ice Show Example"

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SUMMARY

The discussion focuses on calculating total sound intensity and combined sound level in an ice show scenario where music plays at 80.0 dB and a baby yells at 75.0 dB. The total sound intensity is determined using the formula dB = 10log(I/1E-12), resulting in a total intensity of 1.316E-4 W/m². The combined sound level is calculated to be 81.19 dB, demonstrating the logarithmic nature of sound intensity and the importance of using correct logarithmic conversions.

PREREQUISITES
  • Understanding of decibel (dB) scale and sound intensity
  • Familiarity with logarithmic functions and their properties
  • Knowledge of sound intensity formulas, specifically dB = 10log(I/1E-12)
  • Basic skills in algebra for manipulating equations
NEXT STEPS
  • Study the principles of sound intensity and the decibel scale
  • Learn about logarithmic functions and their applications in physics
  • Explore sound level calculations in different environments, such as open vs. enclosed spaces
  • Investigate the effects of sound intensity on human hearing and safety standards
USEFUL FOR

Students studying physics, acoustics professionals, audio engineers, and anyone interested in sound level calculations and their implications for health and safety.

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Homework Statement



A family ice show is held at an enclosed arena. The skaters perform to music with level 80.0 dB. This is too loud for your baby, who yells at 75.0 dB.

(a) What total sound intensity engulfs you?
(b) What is the combined sound level?

Homework Equations



dB = 10log(I/1E-12)

The Attempt at a Solution



I am trying to convert back, but I have never been great with logs, and I cannot figure out how to get I.

80=10log(I/1E-12)
75=10log(I/1E-12)

EDIT - it just clicked - anti-derivatives
A)
75db = 10^7.5/1E12 = I(b)
80db = 10^8/1E12 = I(m)
add them for total = 1.316E-4

B)
10log(1.316E-4/1E-12)
81.19dB
 
Last edited:
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A hint: Use the fact that 10^log x = x
 

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