Estimate the relationship between the maximum and minimum intensity

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SUMMARY

The discussion centers on calculating the relationship between maximum and minimum sound intensity at a point P, located 4 meters from speaker B and 4.123 meters from speaker A. The intensity is determined using the formula I = I0/r^2, where I0 is the intensity at 1 meter from the source. The calculated path difference of 0.123 meters leads to a maximum intensity ratio of approximately 1.941 and a minimum intensity ratio of 0.059, resulting in a final intensity ratio of 4400. The calculations confirm that the intensity fluctuates significantly due to the interference of sound waves from the two speakers.

PREREQUISITES
  • Understanding of sound wave propagation and intensity calculations
  • Familiarity with the inverse square law for sound intensity
  • Knowledge of basic trigonometry to analyze right-angled triangles
  • Ability to perform calculations involving ratios and path differences
NEXT STEPS
  • Study the principles of sound wave interference and its effects on intensity
  • Learn about spherical wave propagation and its mathematical modeling
  • Explore advanced topics in acoustics, such as phase differences and standing waves
  • Investigate real-world applications of sound intensity calculations in audio engineering
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Acoustics students, audio engineers, and anyone interested in the physics of sound wave interactions and intensity calculations.

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Two speakers A and B are separated by 1 meter, the point P is 4 m away from speaker B. If P is a person for what frequency does he hear that the intensity have a minimum?. (The listener hear that the sound intensity reduces and increases).I don't know the distance from P to B. (They form a right-angled triangle)

Estimate the relationship between the maximum and minimum intensity. Assume that there is a spherical wavepropogation and the effect from the surrounding kan be neglected. The speed of sound can be set to 340 m/s. The intensity decreases with 1/r^2 ie the intensity on the wave r m from the source is I0/r^2 where I0(zero) are the intensity on 1m from the distance from the source.

How can i found the intensity and what's about the max and min intensity, what value should i use for that ?

The distance from poit P to A is 4.123 m

I calculated the path difference to be 0.123 m

The answer should be I(max)/I(min) = ca 4400
 
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If I(A) = I(0)/(4.123)^2, I(B) = I(0)/(4.00)^2

I(A)/I(B) = (4.00)^2/(4.123)^2 = 0.941

max= 1+0.941 = 1.941
min=1-0.941=0.059

ratio: 1.941/0.059=32.89

The answer should be 4400

What are i doing that's is wrong ?
 

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