Power of Sound Wave at distance

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SUMMARY

The discussion focuses on calculating sound wave properties from a source located at the top of a 121.5m radio tower. The sound source emits at a frequency of 653.8 Hz with an amplitude of 11.4 nm, while sound travels through air with a density of 1.32 kg/m³ and a velocity of 340 m/s. The participant correctly identifies that the angular velocity can be derived from the frequency, and clarifies that the displacement amplitude (s(max)) is indeed 11.4 nm. Additionally, they confirm that the area (A) should be calculated using the formula 4πr², assuming spherical propagation of sound waves.

PREREQUISITES
  • Understanding of sound wave properties, including frequency and amplitude
  • Knowledge of the wave equation and its components
  • Familiarity with spherical wave propagation concepts
  • Basic proficiency in physics equations related to sound
NEXT STEPS
  • Study the derivation of angular velocity from frequency in wave mechanics
  • Learn about the implications of sound wave amplitude on intensity
  • Explore the effects of air density on sound propagation
  • Investigate the application of the wave equation in different mediums
USEFUL FOR

Students in physics, acoustics researchers, and engineers working with sound wave applications will benefit from this discussion.

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Homework Statement


A sound source is placed at the top of a (h = 121.5m) radio tower. The source has a frequency of 653.8 Hz and an amplitude of 11.4 nm at point A. The air surrounding the tower has a density of 1.32 kgm-3 and sound travels through it with a velocity of 340 ms-1. Point A is 10.8 m above the source. You may ignore any reflections of the sound from the ground.

Homework Equations


P = (1/2) ρAv (ω s( max ) )^2

The Attempt at a Solution


Determine angular velocity from frequency. Sub in density and velocity.
I think A means amplitude and I would put in 11.3nm.
However, s(max) is "displacement amplitude". Does this mean that s(max) = 11.4nm and A= distance from Point A to sound source?
 
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Have been doing some research. A seems to refer to area of the wave sound. So would I be correct in putting A as 4 Pi r squared? Assuming sound is moving out as a sphere?
 
This is indeed the correct method for anyone else who has trouble with this question.
 

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