Number of amplitudes in one wave cycle

[rasen58]

Homework Statement

During one complete cycle, a wave moves through ___ wavelength, ___ period, __ amplitudes

Homework Equations

The Attempt at a Solution

Well I got 1 wavelength, 1 period, and 2 amplitudes
But apparently the answer is 1 wavelength, 1 period, and 4 amplitudes
But I don't see how that's true. The answer even says that 2 is a common mistake, but doesn't really explain why.
If in one cycle, the wave starts at the x-axis, goes up, gown down, and returns on the x-axis, wouldn't that only be 2 amplitudes?

 

[ehild]

Homework Statement

During one complete cycle, a wave moves through ___ wavelength, ___ period, __ amplitudes

Homework Equations

The Attempt at a Solution

Well I got 1 wavelength, 1 period, and 2 amplitudes
But apparently the answer is 1 wavelength, 1 period, and 4 amplitudes
But I don't see how that's true. The answer even says that 2 is a common mistake, but doesn't really explain why.
If in one cycle, the wave starts at the x-axis, goes up, gown down, and returns on the x-axis, wouldn't that only be 2 amplitudes?

I think the problem text is quite wrong. The wave does not move through any amplitude, as its traveling motion is not the same as the displacement during oscillation.
You are right the wave reaches maximal deviation from the equilibrium position during a whole period/wavelength, once in the positive, once in the negative direction. Perhaps the problem writer thought to the answer "1 amplitude" as common mistake.

 

[mfb]

I have never heard "move through its amplitude" before. The amplitude of a wave is a value, giving the maximal value of whatever is oscillating in the wave. How can a way "move through 20 V/m"?
Anyway, 4 is a weird answer and I would expect 2 as answer. The author might have thought of a mechanical wave and counted times of maximal position and velocity separately.

 

[gneill]

The author may have been thinking in terms of the motion of a mass in a mass-spring system. During one cycle the total distance (path length) traveled by the mass is then 4 times the amplitude.

 

[PhysicsCurious]

Hi sorry to bump this old thread but I don't understand how a mass-spring system allows for 4 amplitudes in a cycle.

Can any kind soul help me out?

The author may have been thinking in terms of the motion of a mass in a mass-spring system. During one cycle the total distance (path length) traveled by the mass is then 4 times the amplitude.

 

[mfb]

From "plus 1 amplitude" to "minus 1 amplitude" and back, in total 2*2=4 times the amplitude as motion.

 

[gneill]

Hi sorry to bump this old thread but I don't understand how a mass-spring system allows for 4 amplitudes in a cycle.

Can any kind soul help me out?

Draw and follow the displacement progress of one cycle:

 

[PhysicsCurious]

Thanks people! I just realized it meant the distance that the spring has moved in terms of amplitude instead of how many amplitudes it has reached.

 

[hemangnehra]

Homework Statement

During one complete cycle, a wave moves through ___ wavelength, ___ period, __ amplitudes

Homework Equations

The Attempt at a Solution

Well I got 1 wavelength, 1 period, and 2 amplitudes
But apparently the answer is 1 wavelength, 1 period, and 4 amplitudes
But I don't see how that's true. The answer even says that 2 is a common mistake, but doesn't really explain why.
If in one cycle, the wave starts at the x-axis, goes up, gown down, and returns on the x-axis, wouldn't that only be 2 amplitudes?

Barron's ?...that's why I came here

 

[James R]

The phrasing of the original question doesn't really make sense. For example, the amplitude is the maximum displacement of the particles (or whatever else is "waving") in a wave from some equilibrium position. The wave can't be said to "move through" the amplitude. The amplitude is just a number - usually with some kind of appropriate units depending on what is waving.