How Does Speaker Diffraction Affect Sound Clarity in a Theater?

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SUMMARY

This discussion focuses on the impact of speaker diffraction on sound clarity in a theater setting, specifically involving a diffraction horn loudspeaker positioned 8.1 meters from a row of seats. The speaker operates at a frequency of 20,000 Hz and has an opening width of 0.072 meters. The wavelength of the sound, calculated as 0.01715 meters, is critical in determining sound clarity, as diffraction effects can prevent sound from being heard clearly if the wavelength exceeds the dimensions of obstacles in its path. Participants emphasize the importance of understanding the relationship between wavelength and diffraction, referencing equations such as sin(theta) = lambda / D.

PREREQUISITES
  • Understanding of sound wave properties, including frequency and wavelength.
  • Familiarity with the concept of diffraction in wave physics.
  • Basic knowledge of trigonometric functions, particularly sine.
  • Ability to perform calculations involving velocity, frequency, and wavelength.
NEXT STEPS
  • Study the concept of sound diffraction in detail, using resources like HyperPhysics.
  • Learn how to apply the equation sin(theta) = lambda / D in practical scenarios.
  • Explore the effects of different frequencies on sound clarity in various environments.
  • Investigate additional resources or textbooks that cover wave physics comprehensively.
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Students studying physics, acoustics engineers, theater sound technicians, and anyone interested in the principles of sound propagation and clarity in performance spaces.

sailordragonball
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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?
 
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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.
 
Am I missing an equation?
 
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.
 
Last edited:
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?
 
Last edited:
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?
 
  • #10
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?
 
  • #11
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?
 
  • #12
I solved for lambda ...

... velocity = (lambda * frequency)

... solving for lambda ...

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

... lambda = ( 343 / 2e4 )

... lambda = .01715m
 
  • #13
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?
 
  • #14
It doesn't seem that I'm looking for an angle ... does anyone else have an idea?
 
  • #15
Is there an equation to calculate diffraction?
 

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