Speed of a wave when crossing a boundary vs. not

[Skrphys]

I am having a problem with understanding concepts related to the speed of a wave. Here are my thoughts laid out:
1) The speed of a wave is dependent only on the medium
2) When a wave crosses from a less dense medium into a more dense medium (or visa versa) the speed of the wave is always fastest in the less dense medium.
3) When a wave (particularly a sound wave) is introduced into a medium, the more dense the medium, the faster the wave travels.

These statements seem to be conflicting. Can anyone rectify the situation for me?

Thanks in advance!

 

[ZapperZ]

I am having a problem with understanding concepts related to the speed of a wave. Here are my thoughts laid out:
1) The speed of a wave is dependent only on the medium
2) When a wave crosses from a less dense medium into a more dense medium (or visa versa) the speed of the wave is always fastest in the less dense medium.
3) When a wave (particularly a sound wave) is introduced into a medium, the more dense the medium, the faster the wave travels.

These statements seem to be conflicting. Can anyone rectify the situation for me?

Thanks in advance!

These are two different waves that have different mechanisms.

Light waves actually travel in vacuum. So a "medium" can be naively thought of as "obstacles" in its path.

Sound waves are the oscillation of the medium. So it is the material that make up the medium that oscillates to cause such a wave. Thus, the more dense, the quicker the disturbance is transferred to the neighboring regions.

Zz.

 

[jbriggs444]

2) When a wave crosses from a less dense medium into a more dense medium (or visa versa) the speed of the wave is always fastest in the less dense medium.
3) When a wave (particularly a sound wave) is introduced into a medium, the more dense the medium, the faster the wave travels.

These statements seem to be conflicting. Can anyone rectify the situation for me?

For number 2, you might be imagining a sound wave in helium versus a sound wave in air. Indeed, sound travels more rapidly in helium. And helium is less dense than air. For number 3, you might be imagining a sound wave in steel versus a sound wave in air. Indeed, sound travels more rapidly in steel. And steel is more dense than air.

The speed of a compression wave depends not only on density, but also on stiffness. Sound travels rapidly in steel because steel is very stiff, not because it is very dense. See Wiki.

 

[berkeman]

1) The speed of a wave is dependent only on the medium

Read about "dispersion" of waves in a medium, and maybe update this line?

 

[sophiecentaur]

3) When a wave (particularly a sound wave) is introduced into a medium, the more dense the medium, the faster the wave travels.

Too much of a simplification. In a solid
v = √(K/ρ)
where K is the Stiffness. So , although inversely affected by density, the stiffness counts just as much)
In a gas, the speed of sound is largely dependent on the Temperature. That's because the speed of propagation from molecule to molecule will depend on their individual average speeds.
Bottom line is that there are no general rules and each wave and material needs to be taken on its own.

 

[Skrphys]

Thank you all for your posts. Sometimes I forget that often times in physics approximations are used.