How Far Must Point P Be from Speaker A for Constructive Interference at 400 Hz?

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SUMMARY

The discussion focuses on determining the distance from speaker A to point P for constructive interference of sound waves at a frequency of 400 Hz. The wavelength (λ) is calculated as 0.85 meters using the formula λ = v/f, where v is the speed of sound (340 m/s) and f is the frequency (400 Hz). The equation λ = 2ΔL/(2p-1) is used to find the path difference (ΔL) for the first constructive interference (p = 1), leading to the conclusion that the nearest constructive interference point occurs at a distance of 0.85 meters from speaker A. The discussion also suggests that the smallest x may not correspond to p = 1, indicating further exploration is needed.

PREREQUISITES
  • Understanding of wave interference principles
  • Knowledge of sound wave properties (frequency, wavelength)
  • Familiarity with the speed of sound in air (340 m/s)
  • Ability to apply mathematical equations related to wave behavior
NEXT STEPS
  • Explore the concept of path difference in wave interference
  • Learn about higher-order constructive interference (p > 1)
  • Investigate the effects of varying frequency on constructive interference
  • Study the geometric arrangement of speakers and their impact on sound wave interference
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, acoustics, and sound interference phenomena.

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Homework Statement



Two speakers A and B, sends out sounds at 400 hz

In what distance x between speaker A and the point P is it constructive interference ?

http://s716.photobucket.com/user/Pitoraq/media/Fys2121_zps9a68fef2.png.html

Homework Equations




λ = 2ΔL/(2p-1),

v = 340 m/s

f = 400 Hz

The Attempt at a Solution



λ = 2ΔL/(2p-1),

λ = 340/400 = 0.85 m <==>

lowest constructive interference p = 1

0.85 m = ΔL <==>

0.85 = y - x, where y = (2.5)^2+x^2=y^2 is the distance between P and B.

Is this right ?
 
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That should get you a constructive interference point (node).
I don't think the nearest node to A (i.e., smallest x) occurs for p = 1, though.
 

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