The back wall of an auditorium is 23.0 m from the stage.

if you are seated in the middle row, how much time elapses between a sound from the stage reaching your ear directly and the same sound reaching your ear after reflecting from the back wall? the speed of sound in the air is 343 m/s .

0.067 seconds

Explanation:

The time needed for a person seated in the middle row to receive a sound from the stage, can be calculated assuming that the sound is moving in a straight line at constant speed, taking into account that the distance traveled will be half of the distance between the stage and the back wall:

t₁ = x₁ / v = 11.5 m / 343 m/s = 0.034 sec

The same sound, after reflecting from the back wall, will travel a distance equal to one and a half the distance between the stage and the back wall:

t₂ = 34.5 m /343 m/s = 0.101 sec

The time elapsed between both sounds will be equal to the difference between t₂ and t₁, as follows:

t₂ - t₁ = 0.101 sec - 0.034 sec = 0.067 sec.

since you're a real machine, your ama is always less than your ima, because you can never totally eliminate friction.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(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.