Can someone explain to me these equations of sound waves?

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Discussion Overview

The discussion revolves around the equations related to sound waves, specifically focusing on the meanings of various symbols in the equations for sound intensity and decibel levels. Participants seek clarification on the definitions and implications of these equations, as well as their applications in understanding sound phenomena.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about the meanings of "I" and "A" in the equation I = 1/2 ρ v ω² A², suggesting that ρ represents the density of air, v is the velocity of sound, and ω is the angular frequency.
  • Another participant agrees that "I" likely refers to sound intensity and interprets the second equation β = 10dB * log(I/I0) as relating to changes in intensity in decibels as sound propagates.
  • A suggestion is made to perform a dimensional analysis to explore the units involved, hinting at the relationship between power and area.
  • Clarifications are provided regarding the symbols, with one participant stating that ω stands for angular frequency, I stands for intensity (defined as power per area), and β represents the decibel level as a measure of relative loudness.
  • Links to external resources are shared for further reading on decibel measurements and detailed descriptions of the equations.

Areas of Agreement / Disagreement

Participants generally agree on the meanings of some symbols, such as ω and I, but there remains uncertainty regarding the definitions and implications of the equations as a whole. The discussion does not reach a consensus on all points raised.

Contextual Notes

Some participants note the need for dimensional analysis and the potential for confusion regarding the definitions of intensity and decibels. The discussion reflects varying levels of understanding and interpretation of the equations.

Who May Find This Useful

This discussion may be useful for students or individuals seeking to understand the mathematical representation of sound waves and the concepts of intensity and decibels in acoustics.

Blockade
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I = 1/2 ρ v ω2 A2

I don't know what "I" is nor do I know what "A" is but it has to do with sound waves.
May you also please correct me if I am wrong but is:
ρ = density of air
v = velocity of sound = 343 m/s
ω = angular frequency of the sound wave = 2πƒ

And also may you please answer what is this second equation?:

β = 10dB* log(I/I0) ?
 
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Blockade said:
I = 1/2 ρ v ω2 A2

I don't know what "I" is nor do I know what "A" is but it has to do with sound waves.
May you also please correct me if I am wrong but is:
ρ = density of air
v = velocity of sound = 343 m/s
ω = angular frequency of the sound wave = 2πƒ

And also may you please answer what is this second equation?:

β = 10dB* log(I/I0) ?
I looks to be the sound Intensity. The last equation looks to be the change in Intensity in dB as the sound wave propagates...

Can you post links to where you got the equations from?
 
Do a dimensional analysis.You may find a (time)^-3 term, which is a hint. Just as a wild guess, try units for area for A... then look up the dimensions for power.
Quite often, power ratios are expressed as a logarithm.
 
##\omega## stands for angular frequency which is ##= 2 \pi f## where f ins the frequency.
##I## stands for intensity which is ##= power/area##
##\beta## stands for decibel level which is a relative loudness

This Rutgers lab gets into db measurements and describes the last equation in your post that converts sound intensity relative to a standard baseline intensity to decibels:

https://www.physics.rutgers.edu/ugrad/301/PS08_Intensity_New.pdf

The HyperPhysics book has a description of these equations in great detail:

http://physics.info/intensity/
 
Last edited:

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