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

AI Thread Summary
To calculate the distance an observer must walk to reach a relative maximum in intensity from two speakers separated by 0.7m and driven at 690Hz, the observer's position and path difference must be analyzed. The speed of sound in air is given as 345m/s, leading to a wavelength of 0.5m. The condition for constructive interference requires the path difference to equal an integer multiple of the wavelength. Using the Pythagorean theorem, the relationship between the distances from the observer to each speaker can be established. Solving these equations will yield the required distance the observer must walk to achieve maximum intensity.
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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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