Decibel Comparison Formulas for Sound Levels

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Homework Help Overview

The discussion revolves around comparing sound levels measured in decibels (dB), specifically how to determine the relative loudness of sounds at different dB levels, such as 40 dB, 68 dB, and 0.3 dB.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need for appropriate formulas to compare sound levels and raise questions about the definitions of decibels and the calculations involved in determining loudness differences. Some mention the use of logarithms for non-integer differences in sound levels.

Discussion Status

The conversation is ongoing, with participants exploring definitions and mathematical approaches. Some have provided insights into using logarithmic calculations, while others are seeking clarification on the formulas needed for specific comparisons.

Contextual Notes

There is a reference to external resources for definitions and equations, indicating that participants may be relying on their textbooks or class notes for foundational concepts.

vertciel
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Hello everyone,

Could anyone please show me the appropriate formulas which I need for the following question?

1. How many times louder or softer than sound level of 40 dB is a sound at

a) 68 dB? b) 0.3 dB?


Thank you.
 
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Thanks for your reply.

I know how to calculate the difference in sound level for integers divisible by 10. For example, 60 dB is 10^2 or 100 times louder than 40 dB.

However, I know that I must use logarithms for calculating the difference in sound level for all other integers.
 
Well look at the example of 40 dB

I = 10000 I0, or I = [tex]10^{40dB/10}[/tex] I0 = 10000 I0

and for 60 dB, I = [tex]10^{60dB/10}[/tex] I0 = 106I0

and for 68 dB, ____________?
 
Thank you very much for your help!
 

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