Uncertainty in Wavelength Calculation from Wave Crests on a Pier

[Ryan Hardt]

Homework Statement

Standing in the middle of a 20 m long pier, you notice that at any given instant there are 15 wave crests between the two ends of the pier. Estimate the minimum uncertainty in the wavelength that could be computed from this information.

Homework Equations

[/B]
Uncertainty Principles
ΔxΔp ≥ ħ/2
ΔEΔt ≥ ħ/2

The Attempt at a Solution

I don't really understand how to use the equation to solve the problem. I am given no info on momentum or its uncertainty, and therefore cannot get any relation between the two. Perhaps I am not using the right equations? Any guidance twoards getting the right tools/solving it would be great as there are multiple problems of his ype that I am stuck on, I am fine with doing work myself.

 

[PeroK]

Homework Statement

Standing in the middle of a 20 m long pier, you notice that at any given instant there are 15 wave crests between the two ends of the pier. Estimate the minimum uncertainty in the wavelength that could be computed from this information.

Homework Equations

[/B]
Uncertainty Principles
ΔxΔp ≥ ħ/2
ΔEΔt ≥ ħ/2

The Attempt at a Solution

I don't really understand how to use the equation to solve the problem. I am given no info on momentum or its uncertainty, and therefore cannot get any relation between the two. Perhaps I am not using the right equations? Any guidance twoards getting the right tools/solving it would be great as there are multiple problems of his ype that I am stuck on, I am fine with doing work myself.

Are you sure this is Quantum Mechanics?

 

[Ryan Hardt]

Are you sure this is Quantum Mechanics?

Yes, introduction to quantum. Maybe the problem is being overly simple on purpose (expecting the answer in terms of variables) as I'm quite confused.

Another example:

"The frequency of the alternating voltage produced at electrical generating stations is carefully maintained at 60.000 Hz. How often can the frequency be measured if the reading is to be accurate within 0.010 Hz?"
Perhaps this is a better example.

 

[PeroK]

Yes, introduction to quantum. Maybe the problem is being overly simple on purpose (expecting the answer in terms of variables) as I'm quite confused.

Another example:

"The frequency of the alternating voltage produced at electrical generating stations is carefully maintained at 60.000 Hz. How often can the frequency be measured if the reading is to be accurate within 0.010 Hz?"
Perhaps this is a better example.

Let's stick to the first problem Suppose you were sitting at the seaside and someone said:

That pier is $20m$ long and I can see $15$ wavecrests between the ends, so the wavelength must be $1.33m$. What would you think?

 

[Ryan Hardt]

Let's stick to the first problem Suppose you were sitting at the seaside and someone said:

That pier is $20m$ long and I can see $15$ wavecrests between the ends, so the wavelength must be $1.33m$. What would you think?

Sure I can get a value for the wavelength, but that doesn't really tell me anything about its uncertainty, correct? As its minimum would only change depending on the uncertainty of another measurement with a set ratio related to ħ/2.My attempt at deriving the equation for wavelength uncertainty:

if Δp = h/Δλ

then ΔxΔp ≤ ħ/2

(hΔx)/(ħ/2) ≤ Δλ

4πΔx ≤ Δλ

But this doesn't seem useful as I don't have any info on positional uncertainty.

 

[PeroK]

Sure I can get a value for the wavelength, but that doesn't really tell me anything about its uncertainty, correct? As its minimum would only change depending on the uncertainty of another measurement with a set ratio related to ħ/2.

Do you think that's correct then? The wavelength must be exactly $20m/15$? Leaving asside the HUP.

You can't see any flaw in that calculation?

 

[Jamison Lahman]

Perhaps try thinking about it like this: What is the largest wavelength you can have with 15 waves in a 20m pier? What is the shortest?