Question

1. describe what is needed to form longitudinal standing waves in a slinky and how they are formed.

2. what is the difference between a longitudinal wave and a standing longitudinal wave. how are standing waves formed?

3. explain how sound waves are propagated through air. are these longitudinal or transverse waves?

4. describe the motion of individual air molecules at a node and at an antinode. compare this to the motion of the individual spring coils at nodes and antinodes when a standing wave is produced in a slinky.

5. what is the effect of changing the frequency of the sound? does it change the velocity of the wave? does it change the wavelength?

6. describe the motion of the individual air molecules at a node and at an antinode. compare this to the motion of the individual spring coils at nodes and antinodes when a standing wave is produced in a slinky.

7. what is the effect of changing the frequency of sound. does it change the velocity of the wave? does it change the wavelength?

8. a person who has just inhaled helium gas speaks with a high pitched voice. discuess why this happens given that your larynx and other parts of you respiratory passage act rather like a resonance tube with you vocal chords producing the necessary energy to vibrate the air.

Answer 1

2.

Particles in transverse waves vibrate perpendicular to the direction of the wave and those in longitudinal waves vibrate parallel to the direction of the wave.
Light waves are transverse waves while sound waves are longitudinal.

In general waves are quaternion and contain a real /longitudinal wave and a vector/transverse wave.   

5. and 7.

In general, frequencies have no effect on wave speed.

For electromagnetic waves, speed is always speed of light: 3 * 10 ^ 8 m/s.
This can be shown using Maxwell;s equations (4 equations governing electromegnetism)
By combining the 4 1st order differential equations into 2 2nd order differential equations, you can obtain the wave equation, which governs wave propagation. It was through using this that Maxwell originally discovered that he could calculate the speed of light using measurable quantities (electric permittivity and magnetic permeability)
Frequency definitely does not affect speed here, as this beautiful theory has shown us. Check out Wikipedia: electromagnetism.

The one time when frequency can change wave speed is when electromagnetic waves travel inside materials. Here the electric permittivity (epsilon) and the magnetic permeability (mu) can be frequency dependent.
The speed of light in any material is given by squ.root[1/(epsilon * mu)]. Thus, the speed of waves inside materials can be frequency dependent, but even here, they're more or less constant in frequency ranges that aren't too extreme.

For sound, speed depends on air temperature and pressure (although there may be some extremely small corrections from frequency)
Also, not all frequencies can propagate in a sound wave. In solids, if the frequency is too high, the wave is attenuated (or exponentially damped and it dies.)
This happens because the material cannot support vibrations that high in frequency.

For a wave on a string, the speed is v = squ. root (Tension / mass density).
This is derived in undergraduate level physics textbooks using the loaded string model.
Frequency doesn't play a great role once again.

SIDE NOTE: If you look at ripples on water closely, you'll notice that each individual "wave" travels at twice the speed the entire "group" of waves travels at.
This means that a single wavefront will move from the back of the ripple to the front and fade away :)