Correctly solve this wave related question with step-by-step explanation

[Logistics]

Could someone please have a look at this question+working out and tell me if I did it correctly.

http://people.mail2me.com.au/~benogorancic/que.JPG

 

[OlderDan]

Part B is not correct. From part A you should be able to figure out how far apart the speakers are. Think again about what conditions cause destructive interference, and check the formula that represents those conditions.

 

[Logistics]

I'm sorry but I need more info.

This topic is new to me, been reading all day on the net and nothing :(

 

[OlderDan]

I'm sorry but I need more info.

This topic is new to me, been reading all day on the net and nothing :(

Draw a diagram. Part A says you are on a line between the two speakers, 3 meters from the one on the right and 3.5 meteres from the one on the left. You have correctly calculated the wavelength as .5 meters, so at the starting point the path length difference from the two speakers to where you are is one wavelength. That means you have constructive interference, and that is why the sound is louder.

As you walk into the area in front of the speakers, you will eventually reach a point where the path difference is half a wavelength, or 1.5 wavelengths or 2.5 wavelengths. There you will have destructive interference and you will not be abel to hear. You need to figure out the geometry of that. There is a formula for it. It looks similar to the one you tried to use, but that is not quite it. You cannot use the small angle approximation in this problem. I suggest you just look at the distances involved and basic geometry for this first problem. The application of the formula will make more sense after that.

Edit

I looked at this a bit more carefully. The small angle approximation is not so bad after all. I drew a diagram. The solid arcs are whole number wavelengths from the speakers. The dashed arcs are half way in between, so they are n + 1/2 wavelengths from the speakeers. The blue lines trace the points where the path difference from the two speakers is zero wavelengths, one wavelength, or two wavelengths. The thin black straight line is the path you walk on. Where will destructive interference be encountered? How does that relate to the equation for where destructive interference should be found some distance D from the sources and a distance y from the center line?

Here is a different sort of diagram, and an explanation that will help.

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html

 

[Logistics]

OMG finally got it done, can't believe it ended up so simple arggg omg lol

Thanks for your help