While visiting the albert michelson exhibit at clark university, you notice that a chandelier (which looks remarkably like a simple pendulum) swings back and forth in the breeze once every t = 6.2 seconds.
randomized variablest = 6.2 seconds
(a) calculate the frequency of oscillation (in hertz) of the chandelier.
(b) calculate the angular frequency ω of the chandelier in radians/second. sig. gif? tid=2n74-08-dd-43-8d37-13518no attempt no attempt25% part (c) determine the length l in meters of the chandelier. sig. gif? tid=2n74-08-dd-43-8d37-13518no attempt no attempt25% part (d) that evening, while hanging out in j. j. thompson’s house o’ blues, you notice that (coincidentally) there is a chandelier identical in every way to the one at the michelson exhibit except this one swings back and forth 0.11 seconds slower, so the period is t + 0.11 seconds. determine the acceleration due to gravity in m/s2 at the club.

a) 0,1613 Hz

b) 1,01342 rad/sec

c) 9.5422 m

d)

Explanation:

In the Albert Michelson exhibit at Clark University, we know the period of oscillation of the chandelier is T = 6.2 seconds

The chandelier will be modeled as a simple pendulum

a) Since the frequency is the reciprocal of the period, we have

b) The angular frequency is computed as

c) The period of a simple pendulum is given by

Where L is its length and g is the local acceleration of gravity (assumed 9.8 for this part)

We want to know the length of the pendulum, so we isolate L

d) While hanging out in J.J. Thompson’s House O’ Blues, the new period is 6.2+0.11=6.32 sec. Since the chandelier is the very same (same length), we can assume the gravity is slightly different. We use again the formula for T, but now we'll isolate g as follows

Which results  

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(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.

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