1.) Not sure what type of wave he is talking about - or what precisely he means by motion or source… Typically a wave is a disturbance that involves the continual transfer of energy from one form to another as the disturbance propagates through some medium. For light, energy is transferred between electric and magnetic fields, where for a sound wave, energy is transferred from kinetic energy of a parcel of air, to thermal energy as the next parcel is compressed and so on… For a pendulum, kinetic energy is transferred to potential and back again… But the source is usually some displacement (work) from equilibrium that produces an excess of energy that can then propagate.

2.) I'm guessing that by wave me means a continuous or standing wave - where a pulse is finite in size and in duration.

3.)

T = \frac{1}{\nu}

The period T is inversely proportional to frequency, so if we double the frequency, we halve the period.

4.) As the train moves faster towards you, the sound waves are emitted from locations that are closer and closer to you, which means that each successive wave has a shorter and shorter distance to travel, so while they travel at the same speed through the air, they take less and less time to reach you, so they arrive closer and closer together in time, and the frequency with which the waves arrive is higher.

SInce the speed of sound remains constant, and the frequency increases, the wavelength must decrease…

c = \lambda \nu

5.)

\lambda = \frac{c}{\nu} = \frac{2.99792458 \times 10^8 m/s}{670 nm} {1 \times 10^9 nm}{1 m} \frac{Hz s}{1} = 2.0 \times 10^20 Hz