A tube, open at only one end, is cut into two shorter (nonequal) lengths. The piece that is open at both ends has a fundamental frequency of 422 Hz, while the piece open only at one end has a fundamental frequency of 666 Hz. What is the fundamental frequency of the original tube?

159.1 Hz

Explanation:

The formula for the fundamental frequency of an open pipe is given as,

f' = v/2l' Equation 1

Where f' = fundamental frequency of the open pipe, v = velocity of sound in air, l' = length of the open pipe.

make l' the subject of the equation

l' = v/2f' Equation 2

Given: f' = 422 Hz, v = 343 m/s

Substitute into equation 2

l' = 343/(2×422)

l' = 0.41 m.

Also, for the closed pipe

f = v/4l

Where f = fundamental frequency of the closed pipe, l = length of the closed pipe.

make l the subject of the equation

l = v/4f Equation 4

Given: f = 666 Hz, v = 343 m/s.

Substitute into equation 4

l = 343/(4×666)

l = 0.129 m.

But,

Length of the original tube = l+l' = 0.41+0.129 = 0.539 m.

L = 0.539 m.

Note: The tube is a closed pipe.

F = v/4L Equation 5

Where F = Fundamental frequency of the original tube.

F = 343/(4×0.539)

F = 159.1 Hz.

Hence the fundamental frequency of the original tube = 159.1 Hz

c. convergent boundary.

explanation:

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.