Recent content by Pereskia

The frequency does not increase the current. The frequency do increase the speed of the electrons but the speed of the electrons is not correlated to the current. The charge per unit time depends on how many electrons that is emitted per unit time, not how fast the electrons is moving.

The photon spectrum is continuous but the electromagnetic field consists of light quanta called photons. When it comes to the emission and absorption spectrums, the energy levels of atoms is also quantized. When an excited electron decays (becomes de-excited), the energy that is released in the...

This is the pupils' final project. They choose the subject themself and they do not need to have a final answer to pass. I more see this as an opportunity for them and me to learn as much as possible. It is not every day a pupil comes up with something that is new for me.

Thank you. There is a possibility of vibration in "the cup way" also, then maybe the water acts somewhat as a mass in a spring (or a handle of a cup). It could be harder to make the calculations to see if this is the case but it seems lika a resonable possibility as well.

I can see how the filtering is happening but I can't see how that could affect the base frequency of the note. The pupils have measured the base frequency for a number of water levels and will try to calculate the wave speed that a standing wave (from the bottom up to the water surface) would...

There is of course a sound from the empty bottle as well. There has to be some influence from the water on the standing wave and since the frequency falls with rising water level I guess that the standing wave is mainly in the part of the glass that is below water level. What I can't understand...

Yes, one idea is that the water stabilizes the glass and make a standing wave in the glass possible. But in that case, how does the water do that? Why does the water affect the standing wave in the glass? The pupils will try see if the frequencies match that of a standing wave and what speed...

Two of my pupils in secondary high school is doing a project on the sound generated by striking glass bottles drumsticks. They fill the bottle partially with water and strike the bottle with a drumstick and record the sound. Preliminary results: As long as the water level is in the cylindrical...

You can prove it by contradiction. It is essentially the same proof as the proof of $\sqrt 2$ being irrational. Assume x is rational, then x can be given as $x=p/q$ where p and q have no common primefactors. The equation becomes $$\frac{p^3}{q^3}+\frac{p}{q}+1=0 \Leftrightarrow p^3=-q^2(p+q)$$...

Thank you. I will add this method to my tool box. I will however need the optimum in this case. It will be one part of a larger optimization algorithm. I don't know how the other parts will work with heuristic solutions to the subproblems. Regards David

Hi! Sorry, I want to maximize $\sum_{i=1}^m f_i(n_i)$. I lost the index $i$. Regards David

Hi! (Not sure which forum to pick for this question. This looked like the best one. I apologies if it is not) I have a number of functions (say m functions) with integer domain. All functions are increasing. (Increasing in the sense not decreasing, $f(n+1) \ge f(n)$.) I want an algorithm to...

Hi, Nonreflexive means that the relation is not reflexive. That is there is an x such that $(x,x)\not\in S$. Irreflective is when there is no x such that $(x,x)\in S$ Regards David

Hi, For a vector function you have $$\lim_{x->0} f(x) = 0$$ if and only if $$\lim_{x->0} \Vert f(x)\Vert = 0$$ The norm is needed in the denominator since you can't divide a vector (or scalar) with a vector. Hope this helps David