Two identical speakers (labeled 1 and 2) are playing a tone with a frequency of

Question

Two identical speakers (labeled 1 and 2) are playing a tone with a frequency of 225 Hz. in phase. The centers of the speakers are located 6.00 m apart. Five observers are standing on a line that is 6.00 m in front of the speakers as shown in the figure. Each observer is separated by 1.00 m and Tom is directly in front of speaker 1. Determine which observer or observers will experience constructive interference from the sound emitted by the speakers. The speed of sound is 343 m/s for this problem.

Explanation / Answer

Only Bob experience constructive interefrence.

from the give data

wavelength of the sound wave, lamda = v/f

= 343/225

= 1.52 m

path diffrence of the sound waves reached to Tom, r2 - r1 = sqrt(6^2 + 6^2) - 6

= 2.48 m

= (2.48/1.52)*lamda

= 1.63*lamda

path diffrence of the sound waves reached to Cal, r2 - r1 = sqrt(6^2 + 5^2) - sqrt(6^2 + 1^2)

= 1.73 m

= (1.73/1.52)*lamda

= 1.14*lamda

path diffrence of the sound waves reached to Pam, r2 - r1 = sqrt(6^2 + 4^2) - sqrt(6^2 + 2^2)

= 0.886 m

= (0.886/1.52)*lamda

= 0.582*lamda

path diffrence of the sound waves reached to Bob, r2 - r1 = sqrt(6^2 + 3^2) - sqrt(6^2 + 3^2)

= 0

path diffrence of the sound waves reached to Sue, r2 - r1 = sqrt(6^2 + 4^2) - sqrt(6^2 + 2^2)

= 0.886 m

= (0.886/1.52)*lamda

= 0.582*lamda

we know, for constructive intereference, r2 - r1 = n*lamda (n = 0,1,2,3,4,5.....)

So, Only Bob experience constructive interefrence.

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