Standing Waves

[MedPR]

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When a string vibrates in its second harmonic mode, at what point on the string is the wave speed the fastest?

A. at an antinode
B. at a node
C. In the middle, between the two ends
D. the speed is the same at any point

I assume you can rule out answers A and C, since the middle point of a second harmonic is an antinode, but I don't know between B and D. I want to say D, because

f2=v/l, but I don't know for sure.

 

[milski]

D would be correct. The wave speed is constant over the full length of the string.

 

[SaintJude]

Ok, I know you're right...but what? In other harmonic motions, the speed is maximum when the object is at its equilibrium position.

How do I know when v is max at the eq position vs when v depends on the medium only?

 

[milski]

There are two very distinct speeds that you are talking about. One of them is the speed of the particle (or piece of string, etc.) which moves back and forth. The motion in this case is perpendicular to the sting and has a maximum speed at equilibrium position.

The other is the speed of the propagation of the wave itself. There is no physical particle which moves with that speed, it's the speed of the 'crest of the wave.' The direction in this case is along the string and the speed is constant. Think about it as the speed which determines how soon somebody holding the string further away will fill the motion.

 

[Ssina]

regarding the first case, this is a standing wave at second harmonic, shouldn't the speed be zero at the node?!

 

[MT Headed]

I did want to correct one small issue in the OP's post. A string in a second harmonic is shaped like a figure 8. The point in the middle, like the points at the ends, are called nodes and not antinodes. Not that this has anything to do with answering the question.

 

[MT Headed]

regarding the first case, this is a standing wave at second harmonic, shouldn't the speed be zero at the node?!

Yes, but when the antinodes are flying past the equilibrium position (and the string momentarily appears flat) they are moving at the maximum velocity of any of the particles on the string. And of course the OP's question has nothing to do with this speed, it has to do with the wave speed, which is a constant at all points on the string.

 

[milski]

regarding the first case, this is a standing wave at second harmonic, shouldn't the speed be zero at the node?!

There is no oscillating motion at the node, I can agree with that. But the wave is still moving along the string and bouncing from its end to creating the standing wave. You could say that the speed of the standing wave is zero but that's true everywhere, not only at the node and is not very useful or exciting.

 

[Ssina]

Yes, but when the antinodes are flying past the equilibrium position (and the string momentarily appears flat) they are moving at the maximum velocity of any of the particles on the string. And of course the OP's question has nothing to do with this speed, it has to do with the wave speed, which is a constant at all points on the string.

I agree with the point on OP also.... but I misread what milski said as moving at nodes (vertically i mean).. while s/he was most likely referring to what you said.... thanks for the clarification!

 

[milski]

I agree with the point on OP also.... but I misread what milski said as moving at nodes (vertically i mean).. while s/he was most likely referring to what you said.... thanks for the clarification!

Yes, I was talking about the general case of oscillating motion. Nodes are special. And 'he' would be correct. 😉