Sound attenuation barrier height (trigonometry)

Take the positive root for h2. Solve for h.In summary, the problem is to find dss, dsr, and hs using trigonometry and the given information. The equations used are dss = hs/(sin[θ]), dsr = hs/(sin[∅]), θ = arctan(hs/3.059), and ∅ = arctan(hs/47.191). The given values for Z and d can be used to solve for the height, h, by setting up a quadratic equation and taking the positive root for h.
  • #1
jhmz
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Homework Statement



http://img543.imageshack.us/img543/4598/photosfr.jpg [Broken]

Find dss, dsr and thus hs.

Homework Equations



trig

The Attempt at a Solution


dss = hs/(sin[θ])
dsr = hs/(sin[∅])

dss = 3.059/(cos[θ])
dsr = 47.191/(cos[∅])

θ = arctan(hs/3.059)
∅ = arctan(hs/47.191)

I have tried many times to solve this; usually by substituting the last two equations into the first 4 and trying to solve but without success.

The problem is to do with ISO9613 where Z (path difference between dss+dsr and d) = 7.81 m and d = 50.25 m.

http://www.cevreselgurultu.cevreorm...ps/assessment_methods/industry_ISO_9613-2.pdf (page 21-25)
 
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  • #2
http://img543.imageshack.us/img543/4598/photosfr.jpg [Broken]

OP's image.
 
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  • #3
Let d comprise d1 (dss side) and d2. Write D = dss+dsr.
D = √(d12+h2) + √(d22+h2)
D2 = d12+2h2+d22+2√((d12+h2)(d22+h2))
D2 - d12-2h2-d22=2√((d12+h2)(d22+h2))
Squaring again leaves a quadratic in h2.
 

1. What is a sound attenuation barrier height?

A sound attenuation barrier height is the vertical distance from the ground to the top of the barrier. It is an important factor in determining how effective the barrier will be in reducing sound levels.

2. How does trigonometry relate to sound attenuation barrier height?

Trigonometry is used to calculate the angle of incidence and reflection of sound waves off of a barrier. This information is then used to determine the height needed for the barrier to effectively block or reduce sound.

3. What is the ideal height for a sound attenuation barrier?

The ideal height for a sound attenuation barrier depends on a variety of factors including the distance from the noise source, the type of noise, and the surrounding terrain. Generally, a barrier should be at least as tall as the line of sight between the noise source and the receiver.

4. How does the slope of the barrier affect its height?

The slope of a barrier affects its height by changing the angle of incidence and reflection of sound waves. A steeper slope will require a lower height to achieve the same level of sound reduction as a barrier with a shallower slope.

5. Can sound attenuation barrier height be calculated without using trigonometry?

Yes, there are alternative methods for determining sound attenuation barrier height, such as using empirical data or computer modeling. However, trigonometry is often used because it provides a more accurate and precise calculation.

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