Question

Two speakers emitting identical tones are separated by 3.0 m. A person sits 4.0 m away from one of the speakers. The line from the person to the speaker makes a right angle with the line joining the two speakers. Determine the frequency of the lowest pure tone that will result in
a. constructive interference
b. destructive interference

Answer 1

Given two identical speakers(A,B) are separated by 3.0 m and
The line from the person to the speaker makes a right angle with the line joining the two speakers

completes a right angle triangle,Let the person is perpendicular to speaker B

says that the distance covered by speaker A will be more than by speaker B

there exists some path difference between the sound waves from the speakers reaching the person

for constructive interferance there must be the path difference equal to the integgral multiples of wavelengths

   for lowest frequency the wavelength is longest

path difference = m*lambda

   lambda = path difference /m
  
   lambda = path difference /1 = path difference = 1 m

the frequency is f = v/lambda = 344 m/s/1m = 344 Hz

b) for destructive interference, the path differnce is half integral multiples of wavelength

  
   path difference = (m+0.5)*lambda

the frequency is f = v/lambda = (344 m/s)/(2) m = 172 Hz