A pair of speakers separated by 0.700 m are driven by the same oscillator ata fr

Question

A pair of speakers separated by 0.700 m are driven by the same oscillator ata frequency of 675 Hz. Anobserver, originally positioned at one of the speakers, begins towalk along a line perpendicular to the line joining the speakers.(Assume the speed of sound is 345 m/s.) (a) How far must the observer walk before reaching a relativemaximum in intensity?
m
(b) How far will the observer be from the speaker when the firstrelative minimum is detected in the intensity?
m (a) How far must the observer walk before reaching a relativemaximum in intensity?
m
(b) How far will the observer be from the speaker when the firstrelative minimum is detected in the intensity?
m

Explanation / Answer

   If L is the hypoteneuse of thetriangle and D is the distance between the speakers andx is the distance from the person to the speaker closer tothem then                 m    = L - x             for constructive interference           Or              m   + x   =   L If we square both sides      m22   +   x2 + 2mx =  L2    Using pythag theorem    L2 =   D2   + x2        m22   +   x2 + 2mx   =   D2 + x2        m22  + 2mx  =    D2       m2 *0.51112   +   2 * m * 0.5111 *x = 0.7002        0.26122m2     +    1.0222 m x   = 0.49       x =   ( 0.49   - 0.26122m2 ) / 1.0222 m m is any integer, but x must be a positive number. So we cansee that              0.49 - 0.26122 m2   > 0                          1.75 > m           so wemust have   m = 1     x =   ( 0.49 - 0.26122 * 12 ) / 1.0222 * 1  =             =     0.223 meters Part b works the same way, except that  m   can be   0.5   or  1.5. If you calc both you get    m = 0.5       x=   1.444 meters m = 1.5       x =   0.138 meters        (youuse this one because it's closer to the speaker) Part b works the same way, except that  m   can be   0.5   or  1.5. If you calc both you get    m = 0.5       x=   1.444 meters m = 1.5       x =   0.138 meters        (youuse this one because it's closer to the speaker)

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