Nature and properties of waves

[eureka_beyond]

Homework Statement

This is a general concept question. The problem is, I don't seem to understand what the question is saying and why. Here's the question:

A mechanical wave can propagate through a medium if

a) there are attraction/ repulsion between the medium particles
b) the particles are able to vibrate about their equilibrium position
c) the particles have a net displacement when they are subjected to disturbance

Only a) and b) are correct, but why?

Thanks! =]

Homework Equations

no equations

The Attempt at a Solution

To be specific, I don't understand how there are attraction or repulsion between particles. Then I don't understand how is the vibration of particles important when they are in their equilibrium position. Thirdly, why is c) incorrect. I'm totally confused.

 

[hikaru1221]

1 - Imagine that the particles are like masses and their interaction is like springs attached to them (this is a simple model). If you excite the system by kicking the 1st mass for example, its motion will excite the 2nd mass to move, which will make the 3rd one to move and so on.
If there is no interaction, i.e. attraction or repulsion, it will be an ideal gas. But wave propagating through gas is another story. I guess the question doesn't apply to gas (though wave through gas is mechanical wave), because the answers focus on the vibration of each particle.
2 - They actually always vibrate. Answer (b) means the particles can vibrate, not be in free motion like gas.
3 - I guess answer (c) means the wave makes the equilibrium position change. You know, when vibrating, particles only vibrates about its equilibrium position, so after one period or when the vibration stops, it comes back to the same position, which means no net displacement. But it's just my speculation.

 

[HallsofIvy]

No, the correct answer is NOT (a) and (b), it is (b) and (c). Water waves, for example, occur because, after disturbance, each water "particle" is returned to its position by gravity. There is no "attraction/ repulsion between the medium particles".

 

[eureka_beyond]

Ah~ I better correct the answer in my exercise book. Now I get it why a) is incorrect and why b) is correct. But I'm still having few concerns with c). After disturbance, the particles return to their original position, so there's no net displacement. c) saids there is. So i guess c) must be discribing the situation where during disturbance, there are some particles which does have displacement, and so there is net displacement. It's talking about all the particles as a whole rather than any particular one. Am I right? Or am I just making it more complicated?

 

[rdl]

I would explain the nature and properties of waves as follows:

Waves are a fundamental part of the physical world and can be found in various forms, such as sound, light, and water. They are a type of disturbance that travels through a medium, which can be a solid, liquid, or gas. Waves carry energy from one place to another without actually transporting matter.

One of the key properties of waves is their ability to propagate through a medium. This means that they can travel through a substance, such as air or water, without causing permanent displacement of the particles in that substance. In order for a wave to propagate through a medium, two conditions must be met:

1. Attraction or repulsion between medium particles: In a mechanical wave, such as a sound wave, the particles in the medium are connected to each other through forces of attraction or repulsion. When a disturbance, such as a sound wave, travels through the medium, it causes the particles to vibrate about their equilibrium position. This vibration is essential for the wave to propagate through the medium.

2. Ability to vibrate about their equilibrium position: As mentioned above, the particles in a medium must be able to vibrate about their equilibrium position in order for a wave to propagate through it. This means that the particles can move back and forth around a fixed point without permanently moving away from that point. In other words, the particles must have a restorative force that brings them back to their original position after being disturbed.

As for option c), it is incorrect because it suggests that the particles in the medium have a net displacement when they are subjected to a disturbance. This is not the case for a wave, as the particles only vibrate about their equilibrium position and do not have a permanent displacement. This is a key difference between a wave and a fluid flow, where the particles do have a net displacement.

In summary, the nature and properties of waves involve the ability to propagate through a medium through the vibration of particles about their equilibrium position. Without these conditions, a wave cannot exist or travel through a medium.