Fairy music in Grizedale Forest

One of the installations in Grizedale Forest involves a key that goes through a tree. You have to turn the key 10 times and then music comes out of a speaker in the ground a few metres away. The key clearly turns a generator in the brass disc on the other side of the tree but why 10 turns before you get music? My guess is that you are charging a capacitor from the generator and that when it is charged enough, it can power the speaker circuit. Further evidence for this is that it plays for a while after the key stops turning - presumably whilst the charge runs down.

Periodic pattern in aeroplane contrail

My attention was caught by this contrail. Note the very regular pattern along the far edge. Why is it so regular? Is it due to some periodic motion in the engine? I'd think not guessing that engine frequencies would be too high. And why is it only along one edge? If I see something like this again I need to try to get some idea of the wavelength of the recurring pattern by measuring it against the plane itself.

Lateral inversion jigsaw box

Mrs B realised that the problem she was having with her jigsaw was that the picture on the box was back to front. In other words, it was a mirror image. A mirror causes lateral inversion. Lateral means sideways and inversion means upside down. We don't know whether it was deliberate or not.

Automatic light

 In the circuit above, the battery voltage is shared between the resistance box on the left, which was set to 1000 Ohms, and a light dependent resistor on the right, clipped to the blue board. With light shining on the LDR, its resistance is much lower than 1000 Ohms so it gets less than half of the battery voltage. That's not enough energy to light the LED which is clipped across the LDR.

I put my hand over the LDR to make it dark. The resistance shot up and it got more than half of the battery voltage, enough to light the LED.

I found a wonderful podcast

Just this evening I found out that the physicist and write Sean Carroll is producing a podcast where he talks to some top people. Go here https://www.preposterousuniverse.com/podcast/

Kronecker delta

I'm beginning to get my head round the way that matrices can be written by setting out individual elements within them rather than by writing out the matrix itself. I now realise that when matrices can approach infinitely big sets, then it's just not possible to write them out. In matrix maths, the identity matrix I acts like the number 1 in ordinary arithmetic. I is a diagonal matrix with 1 down the diagonal and 0 everywhere else. So when we don't want to draw matrix, the Kronecker delta symbol is helpful. It = 1 when i=j (so any place that would be on the diagonal of a matrix) but 0 when i and j are not the same numerical value. Sources make it clear that the Kronecker delta is not a matrix but where I see it used, it enables things to be done with individual matrix elements that would require the identity matrix in matrix maths.

Sundials, witches and the eye of God: time in Pendle

 I was interested to spot the small sundial perched on top of the pillar at Newchurch in Pendle. The backstone is not in line with the rest of the church. I think that they have made it face due south to make the angles easier, unlike the one in Radley that I've posted about before. It shows that the church is only approximately west-east in alignment.

 The time theme also plays out with this being the birthplace of Jonas Moore, one of the founders of the Greenwich Observatory which later became the centre of our time system.

And the eye of God? Well, that on the tower in the top picture, left of the bottom of the star decoration. Make of it what you will.

Carboniferous sandstone on Pendle Hill

We climbed Pendle Hill. I was intrigued by the description of the rock as "Carboniferous sandstone". I have normally heard "carboniferous" applied to limestone. It also occurred to me to wonder if the label which was about the UK being in tropical conditions with swamps and coral seas actually applied to the whole world. The answer appears to be "no" if this is anything to go by. https://en.wikipedia.org/wiki/Carboniferous The rocks we found on Pendle were indeed sandy. See particularly the path which is made of rocks dug out of the trench to the side of it. The close up shows large visible grains. Mostly the colour is far paler than the desert sandstones of the the Eden and Wigton area. The suggestion is that these sandstones were deposited in a river delta http://www.kabrna.com/cpgs/stratigraphy/regional_map.htm

LED pavement lights in Blackpool

We found these LED devices on the promenade sea wall by Blackpool Pleasure Beach. They seemed to be worked by small solar panels. The LED I posted about a couple of weeks ago was running 0.02A at 1.5V which is a power of 0.03W or 30mW. There are 6 LEDs so let's estimate 180mW. In peak sunlight, the Sun reaches about 1600 Watts per square metre. On a dull day in Winter maybe 800 Watts per square metre. The solar cell can't be bigger than 2cm x 3cm or 6 x 10^-4 square metres. That would then generate 0.48W in Winter. But the cell doesn't drive the LEDs directly because you want them to come on after dark. It must charge a battery. Then we'd be into calculating Amphours charging versus Amphours discharging.

Making a model of the Levi-Civita Epsilon Tensor

One of the things I have found hard in Quantum Mechanics and in the build up to General Relativity has been the multiple indices used in the notation for multiple dimension spaces. I understand 2-dimensional matrices in the Real number space but have trouble intuiting in higher dimensions. So I try to build models that relate back to the ideas I understand to help me to think that the new idea is "like" a simpler idea in some way. So it was that I came to make a model of the 3-dimensional version of the Levi-Civita tensor. Essentially, it acts in some way like a matrix that assigns a 0, a 1 or a -1 to any multiplication. Obviously, if it is a 0, then the total multiplication is a zero. I used i, j and k coordinates. In my model, i goes to the right, j goes away and k goes up. For any coordinate ijk, you get a zero if any two coordinates are the same. If ijk is 123, 231 or 312 you get a 1. For 321, 213 or 132 you get a -1. You get two none zero entries per vertical or horizontal plane - one is 1 and the other is -1 so it is not quite symmetric - we say anti-symmetric. Now I can visualise it, I need to find out where and how it is used. This was my inspiration https://en.wikipedia.org/wiki/Levi-Civita_symbol#Three_dimensions

Prevalent and Dominant Winds on Hartlepool North Beach

In his book The Pebbles on the Beach, Clarence Ellis makes a distinction between prevalent and dominant winds with reference to their effects on waves. In our latitudes, the prevailing winds come from the south west due to a combination of global-scale convection cells in the air and the Coriolis Effect of the turning planet. On the Atlantic Coast, these winds have miles of ocean to blow over before reaching us, creating huge waves that also travel in from the south west. Here on the east coast, the prevailing wind is coming off the land and cannot therefore be responsible for the waves that break on the shore. When I took the picture on the east coast, the wind was coming from behind me and the waves were coming towards me. For this reason, Ellis would say that the dominant wind would be north east because it is the only one that can cause waves to break on our east coast.

My Very Energetic Maiden Aunt Just Swam Under North Pier

This is North Pier at Hartlepool, seen from South Pier. It reminded me of the mnemonic in the title of this piece, which is used to remember the order of the planets from the Sun. I always preferred it as a mnemonic because it included the Asteroid Belt (A for Aunt!) The problem now is that Pluto has been downgraded to being a "dwarf planet". Pluto belongs to a second belt of small objects left over from the formation of the Solar System which is called the Kuiper Belt. Pluto's problem was that several objects were found that were almost as big as it but wouldn't be called planets, so it had to be downgraded. Find out more about the Kuiper Belt here https://en.wikipedia.org/wiki/Kuiper_belt or listen to Lord Bragg of Wigton's Radio 4 programme about it https://www.bbc.co.uk/programmes/b08g7ttx I was thinking that the mnemonic should be changed to include K for Kuiper Belt but My Very Energetic Maiden Aunt Just Swam Under North Key should really be Quay for it to work.

Experiment to show that water is an insulator

This is one of my favourite experiments. We put ice into a boiling tube and then inserted a piece of gauze to hold the ice down. We then filled up the tube with water. Normally the ice would float - hence the gauze. We gently heated the water at the top of the tube and it boiled. The oddity is holding the tube in your hand to heat it rather than using test tube holders. You'll notice from the picture that we have boiling water at the top but the ice at the bottom has not melted. How is that possible? Thermal energy normally spreads best in fluids by convection. As water is heated, it expands, becomes less dense and floats up. So thermal energy is carried upwards. By heating the tube in the way shown, thermal energy transfer by convection is limited to the very top of the tube. The other way of transferring thermal energy here would be conduction ("heating by particles"). If the tube were metal, you'd burn your hand. But the molecules in water are not joined so they find it hard to pass on the thermal agitation hence thermal energy would take a long time to pass down the tube by conduction. Water is an insulator because it is a bad conductor.

Physics in Advent

The amazing Physics Advent Calendar is back. http://www.physics-in-advent.org/ to get it in English. Toggle switch for language in the top left hand corner of the home page if you want it in German...

Wigton Rugby and the wind turbine

We went up to see Wigton Rugby beat St Benedict's this afternoon and spotted the display for the wind turbine. It will have been up for 10 years next April. It has generated nearly 6000kWh per year. That will be nearly £1000 of electricity per year. It is only a small turbine but it will have paid for itself and more.