How Does Speaker Diffraction Affect Sound Clarity in a Theater?

[sailordragonball]

Diffraction or Distraction??

A row of seats is parallel to a stage at a distance of 8.1 m from it. At the center and front of the stage is a diffraction horn loudspeaker. This speaker sends out its sound through an opening that is like a small doorway with a width D of 0.072 m. The speaker is playing a tone that has a frequency of 2.0 104 Hz. The speed of sound is 343 m/s. What is the separation between two seats, located near the center of the row, at which the tone cannot be heard?

 

[berkeman]

You need to show your work in order for us to help you.

 

[sailordragonball]

Oops, I forgot to add that ... LOL ...

D = 0.072m (given)
f = 2.0 X 10^4 Hz or 20,000 Hz
v = 343 m/s (given)

... I know for the second part ... sin (theta) = (lambda / D)

... solving for lambda ... lambda = velocity / frequency ...

... lambda = 343 / 20000

... therefore: lambda = .01715m... this is where I'm stuck.

 

[sailordragonball]

Am I missing an equation?

 

[dontdisturbmycircles]

If the wavelength of a sound is bigger than the person/object/insect/whatever it is hitting, the sound won't be heard/clear. Also if there is not enough room for the wavelength to pass through, it will not work either (diffraction), apply this concept to your problem.

 

[sailordragonball]

I don't understand ... I was reading from my Cutnell and Johnson 7th edition physics book - but, I couldn't understand the diffraction concept ... can you elaborate?

 

[dontdisturbmycircles]

http://en.wikipedia.org/wiki/Diffraction

Take a look at that link. You do know that 'lambda' $$\lambda$$ is the symbol for wave length right?

 

[dontdisturbmycircles]

Here is an even better link

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/diffrac.html

 

[sailordragonball]

I went to the Hyperphysics website ... and got the jist of it ... but, it's not clear to me yet ... any other suggestions or walkthroughs?

 

[dontdisturbmycircles]

Read those pages over and over until you get it, alternatively you can search on google for "diffraction". I think that between your textbook and the two websites you should have enough information to grasp the concept. What exactly don't you understand about it?

 

[sailordragonball]

I'm more of a "hands-on" math concept guy ... rotational kinematics and torques killed me last chapter ... I don't know what equations to use to set up a problem. Make sense?

 

[sailordragonball]

I solved for lambda ...

... velocity = (lambda * frequency)

... solving for lambda ...

... lambda = (velocity / frequency) ...

... lambda = ( 343 / 2e4 )

... lambda = .01715m

 

[sailordragonball]

I know ...

... sin of theta = lambda / D

... therefore, I concluded with ...

... sin of theta = ( .01715 / .072 )

... sin of theta = .238 ...

... but, I'm not trying to find an angle ... am I?

 

[sailordragonball]

It doesn't seem that I'm looking for an angle ... does anyone else have an idea?

 

[sailordragonball]

Is there an equation to calculate diffraction?