music

Constructive interference at Frequency, Kings Cross

exterior of Frequency Kings Cross

Note the tiles. Frequency, Kings Cross on a rainy day.

It was a rainy afternoon when we ventured to Kings Cross and into Frequency. Suggested by the London’s Best Coffee App as the closest café to our then location, we made our way through puddles and rain onto Kings Cross Road. At that point, a brain-freeze meant that we couldn’t see where Frequency should be. The map on the app was implying that we were extremely close but there didn’t seem to be a café around. Then we saw it in front of us! The striking black and white tiling on the floor somehow hiding this shop-front from view.

The tables inside matched the tiling outside. Black and white triangles meeting at a point. My long black (from Workshop) was placed close to the intersection of these triangles. The coffee arrived in a mug, more cylindrical than standard coffee cups and so closer to mathematical models of coffee cups that are used in explanations of convection and rotation in the cups. An interesting change of aesthetic that also changes the internal dynamics of the coffee. A nice touch was that the mugs were also coordinated with the tiling, though to be fair I hadn’t noticed that at the time.

The coffee itself was extremely fruity, a lovely warming brew to enjoy while watching the rain outside. The interior of the café meanwhile was decorated with a lot of wood around together with a couple of music stands. Perhaps the music stands make sense in a café named Frequency. Indeed, according to the review on London’s Best Coffee (or as it is now known, Best Coffee), there are plans to build a music recording studio here as well as having live musical performances. However, also mentioned in that review was the fact that this café had been designed and built from scratch with the help only of online tutorials. Which makes a particularly resonant connection with something I noticed here.

mug of coffee at Frequency

Coffee at Frequency.

What caught my eye as I contemplated this café was the one bit of bright colour on the ceiling. It was also something that hints at problems that can crop up when you design and build your own electrical circuits: Parallel wires (in this case leading to the lightbulbs). Perhaps in the café, these were intended to represent music staves, certainly that would fit in the theme. However to an experimental physicist who dabbles in designing pieces of kit for electrical measurements, these parallel lines leading to a light mean something entirely different.

They mean noise.

When you are designing a piece of electrical equipment to be used for measuring voltages across an unknown material, there often ends up being a lot of wiring in the probe as well as the bit at the end of the instrument that you are actually interested in. Some of this has a practical purpose. Often we want to measure something when it is very cold so it has to be on the end of a metal rod that is inserted into a vat of liquid nitrogen or helium or that is held in a strong magnetic field. When designing the probe, the bits of wire leading to the interesting bit at the end of the rod can be almost as important to consider as the measuring bit itself.

To see why, perhaps you remember putting compasses around a wire carrying an electric current? As the electric current is switched on, the compass needles move indicating that the electrical current generates a magnetic field. The basis of electric motors and dynamos, the idea is that an electrical current will generate a magnetic field and a moving magnetic field would generate an electrical current.

transmission lines, electrical noise

The wires to the light bulbs in Frequency Kings Cross. Memories of transmission line lab experiments.

Now, imagine two parallel wires each carrying an electrical current. Both of them will produce a magnetic field, but if there is a varying current in one or other of the wires, the magnetic field will also be varying. And if there’s a varying magnetic field, it can induce a current in the neighbouring wire. In this way, electrical noise on one of the wires can be transmitted to the other.

Such electrical noise can be inconvenient if we are trying to speak on the phone and just hear a ‘hiss’, or if we are trying to listen to the radio and just can’t tune in. It could also be more problematic, imagine if there was a lot of electric noise on a machine measuring the electrical activity of your heart, an ECG. Consequently, there are whole books written on how to reduce electrical noise pick up. However one simple way to reduce a lot of the noise is to get rid of those parallel lines the like of which are on the ceiling at Frequency by twisting them together. The ‘twisted pair’ is a great way of making more sensitive electrical measurements. And if you wanted to reduce the noise further, you can shield the twisted pair with another conductor and ground (or earth) it.

The twisted pair works by reducing the magnetic coupling between the two wires. Of course, it may not be quite as immediately aesthetically pleasing as parallel wires on a ceiling but there is something quite elegant about a well made and shielded twisted pair properly grounded in an electrical circuit. And when you put everything together, ground it properly and see the noise from the electrical mains (at 50Hz) disappear, there is a certain pleasing effect from that too.

Café design as a clue to electrical design. Frequency can be found at 121 Kings Cross Road, WC1X

 

The hot chocolate effect

hot chocolate effect, Raphas

A ready prepared hot chocolate

This is an effect that reveals how sound travels in liquids. It enables us to understand the milk steaming process involved in making lattes and yet, it can be studied in your kitchen. It has an alternative name, “The instant coffee effect”, but we won’t mention that on this website any further. To study it you will need,

1) a mug (cylindrical is preferable),
2) some hot chocolate powder (no, instant coffee really will not do even if it does work)
3) a teaspoon
4) a wooden chopstick (optional, you can use your knuckle)

Make the hot chocolate as you usually would and stir. Then, remove the spoon and repeatedly tap on the bottom of the mug with the wooden chopstick (you could instead use your knuckle). Over the course of about a minute, you will hear the note made by the chopstick rise (not having a musical ear, I will have to trust that this can be by as much as three octaves).

resonator, mouth organ

The length of the pipes in this mouth organ determine the note heard. Photo © The Trustees of the British Museum

What is happening? Well, just like an organ pipe, the hot chocolate mug acts as a resonator. As the bottom surface of the hot chocolate is fixed in the mug and the top surface is open to the air, the lowest frequency of sound wave that the hot chocolate resonator sustains is a quarter wavelength. The note that you hear depends not just on the wavelength, but also on the speed of sound in the hot chocolate, and it is this last bit that is changing. When you put in the water and stir, you introduce air bubbles into the drink. With time (and with tapping the bottom surface), the air bubbles leave the hot chocolate. The speed of sound in a hot chocolate/air bubble mixture is lower than the speed of sound in hot chocolate without air bubbles. Consequently, the frequency of the note you hear is higher in the hot chocolate without bubbles than in the former case.

Let’s use this to make a prediction about what happens when a barista steams milk ready for a latte. At first, the steam wand introduces air and bubbles into the mixture but it is not yet warming the milk considerably. From above, we expect that the speed of sound will decrease as the bubbles are introduced. This will have the effect of making the ‘note’ that you hear on steaming the milk, lower. At the same time the resonator size is increasing (as the new bubbles push the liquid up the sides of the pitcher). This too will act to decrease the note that is heard as you steam (though the froth will also act to damp the vibration, we’ll neglect this effect for the first approximation). At a certain point, the steam wand will start to heat the milk. The speed of sound increases with the temperature of the milk and so the note will get higher as the milk gets warmer.

So this is my prediction, musically inclined baristas can tell me if there is any truth in this:

1) On initially putting the steam wand into the cold milk, the tone of the note heard as the milk is steamed, will decrease.
2) This decrease will continue for some time until the milk starts to get warm when the note increases again.
3) Towards the end of the process, the note heard on steaming the milk will continue to increase until you stop frothing.
4) It should be possible, by listening to the milk being steamed, to know when the milk is ready for your latte just by listening to it (if you are experienced and always use similar amounts of milk per latte drink).

So, let me know if this is right and, if it is wrong, why not let me know what you think is happening instead. I’d be interested to know your insights into the hot chocolate effect in a milk pitcher.