Calculating Relative Maximum for Sound Waves from Speakers Separated by .7m

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SUMMARY

The discussion focuses on calculating the distance an observer must walk to reach a relative maximum in sound intensity from two speakers separated by 0.700m, driven by a 690Hz oscillator. The observer's position is analyzed using the principles of constructive interference, where the path difference CB - CA equals the wavelength (0.5m). The Pythagorean theorem is applied to relate the distances from the observer to the speakers, leading to the equation CB² - CA² = AB². The solution involves solving these equations to find the distance CA.

PREREQUISITES
  • Understanding of wave interference principles, specifically constructive interference.
  • Knowledge of the Pythagorean theorem and its application in physics.
  • Familiarity with sound wave properties, including frequency and wavelength calculations.
  • Basic algebra skills for solving equations involving distances.
NEXT STEPS
  • Study the principles of wave interference in more detail, focusing on constructive and destructive interference.
  • Learn how to calculate wavelength from frequency using the formula λ = v/f, specifically for sound waves.
  • Explore practical applications of the Pythagorean theorem in physics problems involving distances and angles.
  • Investigate the effects of speaker placement on sound intensity and interference patterns in acoustics.
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics and sound, as well as educators seeking to explain concepts of sound interference and intensity maximization.

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Homework Statement


A pair of speakers separatd by .700m are driven by the same oscillator at a frequency of 690Hz. An observer originally positioned at one of the speakers begins to walk along a line perpindicular to the line joining the speakers. How far mus the observer walk before reaching a relative maximum in intensity


Homework Equations



v(air)=345m/s

r2-r1=n(lambda)

The Attempt at a Solution



How do i figure out the r values when only one side is given? I know i should use the pythagorean theorem here. I also know a relative maximum is constructive interference so i will use a full integer for n. r2-r2=1(lambda). I'm not sure what I'm missing here.

i have:
f=690Hz
lambda=.5m
T=.0015s

suggestions would be appreciated.
thanks
 
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Let A an B are the positions of speakers and C is the position of the observer. When observer listenes maximum intensity, the path difference CB -CA = lamda = 0.5 m. According to pythagorean theorem CB^2 - CA^2 = AB^2. Solve these equations and find the distance CA of the observer.
 

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