In summary, the author suggests that physics teachers use two different methods to help students find limits on quantities: telling them where the limits lie or having the students experiment and find the limits themselves.
Redbelly98
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Introduction
Physics teachers who are either writing physics questions that deal with waves on a string or setting up equipment for a class lab or demo of standing waves on a string might find the following analysis useful. When writing questions for physics tests or homework, it is preferable to use physically plausible values for any quantities (Ref. 1). With that in mind, let us explore what physically limits quantities such as wave speed or string tension in a typical standing-wave setup for a school physics lab.

The above figure shows a typical standing-wave setup. An oscillator at one end of a string vibrates vertically to produce waves along the string, while the weight hanging at the other end holds the string taut. A pulley confines the waves to the horizontal section of the string while still allowing the force exerted by the weight to hold the string taught.
The...

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Drakkith, berkeman, BvU and 5 others
I'm particularly interested in hearing from physics teachers or students who have used these setups, especially if your setup was outside what I'm calling the "physically reasonable zone".

Redbelly98 said:
if your setup was outside what I'm calling the "physically reasonable zone".
I'm not sure what you mean by that expression, exactly but I have used an alternative method which might interest you. The method involves electromagnetic force. A nice beefy horseshoe magnet is placed with a stretched steel wire held between the poles. One end is fixed and the other is tensioned with a variable mass. A fairly powerful signal generator is connected across the ends of the wire. Not directly on the wire but to the fixing and pulley so that the excitation is 'clean' and can be applied at any point along the wire. I prefer this method because, unlike when the end of the string is moved, the precise wavelength can be measured because true Nodes can be seen at each end.
Good magnets are easily obtainable these days - much better ones than what I had available a few years ago and a standard School Oscillator will give you frequencies from a few Hz to a few tens of Hz.
Give it a go.

Redbelly98 and vanhees71
Oh, cool setup!
sophiecentaur said:
I'm not sure what you mean by that expression ...
I was referring to the two diagrams toward the of the article -- to see them, you'd need to click the "Continue reading" link. (Not sure if you didn't see the diagrams, or did see them and something still isn't clear about them.)

Redbelly98 said:
(Not sure if you didn't see the diagrams, or did see them and something still isn't clear about them
Ah yes - I see where you're coming from. now. Choosing suitable ranges of variables to present to students for practical exercises can be approached in two ways. you either tell them to look between specified limits or you tell them to find those limits. Personally, I always found it difficult to find students with enough confidence to do the latter. They always wanted guidance and we seldom had time to do any more than the basic experiment, followed by the customary graph and analysis. I sometimes wonder if it had anything to do with the religious basis on which the School was run - but that could be just me offloading some of my own guilt.
Afair, there were only one or two opportunities for extended investigations and there would only be the occasional student who would actually risk writing their own agenda. When that occurs, of course, it's great.
Spotting where the experiment breaks down - where the graph leaves the straight line, for instance is good for qualitative comments.

Earlier in life, as a Research Engineer, I was always coming across this sort of thing but I think experiments would have been run, using ranges of variables that were realistic, found during the experiment on an iterative basis (seat of pants, you could say).

vanhees71

## 1. What is a wave on a string?

A wave on a string is a disturbance or oscillation that travels through a medium, such as a string, in a predictable and periodic manner. This type of wave is also known as a transverse wave, as the motion of the particles in the medium is perpendicular to the direction of the wave's propagation.

## 2. What are the physical properties of a wave on a string?

The physical properties of a wave on a string include amplitude, wavelength, frequency, and speed. The amplitude is the maximum displacement of the string from its equilibrium position, the wavelength is the distance between two consecutive points on the string that are in phase, the frequency is the number of complete oscillations the wave makes in one second, and the speed is the rate at which the wave travels through the string.

## 3. How is the speed of a wave on a string determined?

The speed of a wave on a string is determined by the tension and mass per unit length of the string. The higher the tension and the lower the mass per unit length, the faster the wave will travel through the string. This relationship is described by the equation v = √(T/μ), where v is the speed, T is the tension, and μ is the mass per unit length of the string.

## 4. What is the relationship between frequency and wavelength in a wave on a string?

The frequency and wavelength of a wave on a string are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation v = fλ, where v is the speed, f is the frequency, and λ is the wavelength.

## 5. How does the amplitude of a wave on a string affect its energy?

The amplitude of a wave on a string is directly proportional to its energy. This means that as the amplitude increases, the energy of the wave also increases. The energy of a wave on a string is determined by the square of its amplitude, so a doubling of the amplitude will result in a quadrupling of the energy. This relationship is described by the equation E ∝ A^2, where E is the energy and A is the amplitude.

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