Which of the following statements characterizing types of waves are true?

(a) mechanical waves require a medium through which to propagate.
(b) mechanical waves can be either longitudinal, transverse, or some combination of the two
(c) the displacement of particles in a transverse wave is along the axis of the wave propagation.
(d) wavelength is used to characterize transverse waves, but not longitudinal waves

a and b.

Explanation:

In general  types of wave

1. Transverse wave  :

    In these waves particle are vibrate perpendicular to motion of waves.

 Ex : Electromagnetic wave , Radio wave .

2. Longitudinal wave :

   In these waves particle are vibrate along the motion of waves.

 Ex : Sound wave

Mechanical wave  :

1 .These are transverse wave or Longitudinal wave or combination of them .

2.These waves required medium for propagation.

3. The particle are vibrate perpendicular to motion of waves.

So the option a and b are correct.

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.

the answer is a. hope this .