Question

Two speakers, 1 and 2, are set up with their centers 6.00 m apart. Both are playing the same tone of frequency 225 Hz, in phase. Five listeners are standing on a line that is 6.00 m in front of the speakers as shown in the figure. Each listener is separated by 1.00 m and Cal is directly in front of speaker 1. Determine which listener or listeners will experience constructive interference from the sound emitted by the speakers. The speed of sound is 343 m/s for this problem. Sue Cal Tom Bob Pam

Answer 1

Sue experuence construtive interefrence

from the given data,

wavelength of the sound wave, lamda = v/f

= 343/225

= 1.524 m

path difference at the location of call, r2 - r1 = sqrt(2)*6 - 6

= 2.485 m

path difference at the location of pam, r2 - r1 = sqrt(6^2 + 5^2) - sqrt(6^2+1^2)

= 1.727 m

path difference at the location of Bob, r2 - r1 = sqrt(6^2 + 4^2) - sqrt(6^2+2^2)

= 0.886 m

path difference at the location of Sue, r2 - r1 = sqrt(6^2 + 3^2) - sqrt(6^2+3^2)

= 0 m

path difference at the location of Tom, r2 - r1 = sqrt(6^2 + 4^2) - sqrt(6^2+2^2)

= 0.886 m

for constructive interefrence path difference should be = n*lamda (n = 0,1,2,3,4,5...)

so, Sue experuence construtive interefrence