Question

Speaker A is sounding a single tone in phase with speaker B (see figure below). The two speakers are separated by 8 m. What intensity level will you hear if you are located 6 m in front of speaker A and the frequency of the tone is 1372 Hz? Assume that the 40-W speakers can be approximated as point sources and the speed of sound is 343 m/s.

_________dB

Answer 1

given power P = 40 W

velocity v = 343 m/s

r = 6 m

the intensity I = P /A

here A = 4 r²

and I = ( I₁² + I₂² + 2 I₁ I₂ cos )

I₁ = P / A = 40 / 4 X 3.13 X 6²   

I₁ = 0.08846 W/m²

and the distance = ( 8² + 6² )^1/2 = 10

I₂ = P / A

= 40 / 4 X 3.14 X 10²

I₂ = 0.03184 W/m²  

= tan^-1 ( I₂ / I₁ )

= tan^-1 ( 0.0318 / 0.08846 )

= 19.77^o

there fore intensity is " I "

I = ( 0.08846² + 0.0318² + 2 X 0.08846 X 0.0318 X cos19.77 )

I = 0.118873 W/m²

or

I = 110.751 dB