How intensity and amplitude depends from a distance r

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SUMMARY

The discussion focuses on the relationship between intensity and amplitude of sound waves emitted from a line source, specifically a noisy freight train. It establishes that intensity (I) is inversely proportional to the square of the distance (r) from the source, expressed as I ∝ r⁻². The area of the sound wave's influence is modeled as a circular cone, leading to the conclusion that as distance increases, intensity decreases significantly. The amplitude of the wave is also affected by this distance, although the exact relationship was not fully explored in the discussion.

PREREQUISITES
  • Understanding of sound wave propagation
  • Knowledge of intensity and amplitude in acoustics
  • Familiarity with the concept of cylindrical sound waves
  • Basic mathematical skills for area calculations
NEXT STEPS
  • Research the mathematical derivation of sound intensity from a line source
  • Learn about the relationship between amplitude and intensity in sound waves
  • Explore the effects of distance on sound wave propagation in different mediums
  • Investigate real-world applications of sound intensity calculations in engineering
USEFUL FOR

Students studying physics, acoustics researchers, and engineers involved in sound design or noise control will benefit from this discussion.

AndreAo
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Homework Statement


A line source of sound (for instance, a noisy freight train on a straight track) emits a cylindrical expanding sound wave. Assuming that the air absorbs no energy, find how (a) the intensity I and (b) the amplitude sm of the wave depends on the perpendicular distance r from the source.

Homework Equations


Intensity = Power/Area

The Attempt at a Solution


I thought that the area would be something like the base of a circular cone, and the area of it base would A [tex]\propto[/tex] r². Then I [tex]\propto[/tex] r⁻². Is the reasoning right?
 
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what is this？I totally confused
 
A relatively ancient (yr 2009) post that had no replies. Likely no-one at the time could interpret the problem statement cogently either. Best to just move on and let it rest.
 

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