A person stands in an open space listening to the sound from two speakers. The speakers generate sound with a frequency of 489.5 Hz, the speed of sound in air is 343 m/s. The speakers are 2.00 m apart and the person walks away from one of the speakers along a line that is perpendicular to a line drawn between the two speakers as shown in the diagram. The person starts 1.00 m from the first speaker. What distance does the person need to walk along the straight line in order to hear the first local maximum in sound intensity due to the interference of the two waves?
y = Asin(kx - wt)
v = f*lambda
c^2 = a^2 + b^2 (Maybe??)
The Attempt at a Solution
Since there is an interference between the two waves, i thought you can calculate the addition of the two wave equations. Since both waves have the same equation, it will come out to y = 2Asin(kx-wt), where k = 2pi*343m/s/489.5Hz and k = 2pi*489.5Hz. Since y = 0 at the first wavelength, which is 343m/s/489.5Hz, you can substitute that in to find t, but realised that i was going nowhere because i dont know the amplitude... Am i going in the right direction by adding the two equations?
Also, how does wave superposition work if one wave comes in at an angle to the other? Are there different equations for the addition of them? Or do the waves just not superimpose?