Determining interference pattern for two loudspeakers

[twinklestar28]

Homework Statement

Two loudspeakers, at the same height are 2m apart and in phase with each other.Both emit 705Hz sound waves into a room. A listener stands 5m in front of the loudspeakers and 2m to one side of the centre.

a) Is the interference pattern at this point constructive,destructive or something in between?

b) How would the situation differ if the outputs of the loudspeakers were 180 ° out of phase?

Homework Equations

Path difference=L1-L2
λ=v/f

The Attempt at a Solution

a) λ=343m/s / 705Hz = 0.486m

Doing Pythagoras on both lengths I get L1=√5^2 +3^2 = √34m
L2=√5^2+1^2 = √26m

path difference=√34-√26, dividing by wavelength gives 1.504409122 so can i round that to say that m=1.5 hence there is destructive interference or do I leave the value like that and say it is something in between?

b) phase difference=∏=mλ=path difference = m=∏-0.7319/ 0.486 = 4.958

Again can I round up to say that m=5 so there is constructive interference since there the number of wavelengths is a whole integer.

A bit confused on the values I am getting and whether I can round, could someone check my answers?

 

[berkeman]

Homework Statement

Two loudspeakers, at the same height are 2m apart and in phase with each other.Both emit 705Hz sound waves into a room. A listener stands 5m in front of the loudspeakers and 2m to one side of the centre.

a) Is the interference pattern at this point constructive,destructive or something in between?

b) How would the situation differ if the outputs of the loudspeakers were 180 ° out of phase?

Homework Equations

Path difference=L1-L2
λ=v/f

The Attempt at a Solution

a) λ=343m/s / 705Hz = 0.486m

Doing Pythagoras on both lengths I get L1=√5^2 +3^2 = √34m
L2=√5^2+1^2 = √26m

path difference=√34-√26, dividing by wavelength gives 1.504409122 so can i round that to say that m=1.5 hence there is destructive interference or do I leave the value like that and say it is something in between?

b) phase difference=∏=mλ=path difference = m=∏-0.7319/ 0.486 = 4.958

Again can I round up to say that m=5 so there is constructive interference since there the number of wavelengths is a whole integer.

A bit confused on the values I am getting and whether I can round, could someone check my answers?

I think you have it right. The differences are less than a percent from full destructive and constructive interference, so I'd go with those answers myself.

 

[twinklestar28]

Ok, thanks :)