Final answer:
The Fresnel Number (N) for a 5.00m high noise barrier causing a Path Length Difference of 1.4108m for a 1000 hertz frequency is calculated using the wavelength of the sound and the dimensions given. The Fresnel Number is 51.653 when calculated to three decimal places.
Step-by-step explanation:
The student is asking how to calculate the Fresnel Number (N) in a scenario where a 5.00m high noise barrier causes a Path Length Difference of 1.4108m for noise at a frequency of 1000 hertz. To find the Fresnel Number, we use the equation:
N = (a2)/Lλ
where a is the width of the aperture (in this case, the height of the noise barrier), L is the Path Length Difference, and λ is the wavelength of the sound. First, we need to calculate the wavelength λ of the sound using the speed of sound, v = 343 m/s, and the frequency f = 1000 Hz:
λ = v / f = 343 m/s / 1000 Hz = 0.343 m
Then we can substitute the values into the Fresnel Number equation:
N = (5.00m)2 / (1.4108m)(0.343m) = 25.00 / 0.484m2 = 51.6528925
So, the Fresnel Number for this scenario to three decimal places is:
N = 51.653