Category: science

Some predictions come true

In the April, 1968 issue of Wireless World, there is a short article titled “P.C.M. Copes with Everything”

It’s interesting reading the 57-year old predictions in here. One has proven to be not-quite-correct:

While 27 levels are quite adequate for telephonic speech,
211 or 212 need to be used for high quality music.

I doubt that anyone today would be convinced that 11- or 12-bit PCM would deserve the classification of “high quality”. Although some of my earliest digital recordings were made on a Sony PCM 2500 DAT machine, with an ADC that was only reliable down to about 12 or 13 bits, I wouldn’t try to pass those off as “high quality” recordings.

But, towards the end of the article, it says:

The closing talk was given by A. H. Reeves, the inventor of p.c.m. Letting his imagination take over, he spoke of a world in the not too distant future where communication links will permit people to carry out many jobs from the comfort of their homes, conferences using closed-circuit television etc. For this, he said, reliable links capable of bit rates of the order of 109 or 1010 bits will be required. Light is the most probable answer.

Impressive that, in 1968, Reeves predicted fibre optic connections to our houses and the ability to sit at home on Teams meetings (or Facetime or Zoom or Skype, or whatever…)

Data sonification

Back when I was at McGill, one of my fellow Ph.D. students was Mark Ballora, who did his doctorate in converting heart rate data to an audible signal that helped doctors to easily diagnose patients suffering from sleep apnea.

This article from Science magazine in 2017 talked about Mark’s later work sonifying astronomical data, but I was reminded of it in a recent article on the BBC about researchers doing the same kind of work.

Speed Math

Two math puzzles:

#1: You have to drive to a meet someone at a specific time. Let’s say that you only have to drive on one road to get there, and the speed limit is the same the whole way. You calculate the time it will take to get there on time, and you start driving – but there’s traffic. So, you wind up driving half the distance at half the speed, then the traffic disappears.

How fast do you have to go the rest of the way to arrive at the meeting on time?

#2: You’re driving on a two-lane highway where the speed limit is 70 km/h. You are driving 100 km/h, and you pull into the left lane to pass someone who is driving the speed limit. Everything about the car you’re passing is identical to yours – even the driver weighs the same as you do. At the instant that you are side-by side, a train appears across the road in front of you and stops. You both hit the brakes at exactly the same time to try and stop from hitting the train.

Luckily, the person in the other car stops just as his bumper touches the train, let’s say 1 mm before touching it… But, because you were driving faster, you cannot stop in time.

How fast are you going when you hit the train?

The answers

#1. Most people instinctively say “double the speed limit” to make up the lost time. However, this is not the right answer.

Let’s say that the meeting is 100 km away, and the speed limit is 100 km/h. Therefore, it should take you 1 hour to get to the meeting.

If you drive half the distance (50 km) at half the speed (50 km/h), then at the moment the traffic clears up, you should have been at your destination. So, you would have to drive infinity km/h to get there. However, since teleportation doesn’t exist yet, you might as well just call and tell them you’ll be late.

#2: This one is a little tougher, but it should be pretty intuitive for someone working in audio. A car’s brakes work by taking the energy in the car’s momentum, and converting that to heat in the brake discs. The key word there is energy.

So, the question is: if you consider the amount of energy removed from the car going 70 km/h, and take that out of the energy in the car going 100 km/h, how much energy is left?

The answer is 70 km/h. For someone in audio, this might look like a familiar answer, since 0.7 V has half of the power of 1.0 V (assuming identical loads). In the case of the cars, it’s because the amount of power (the amount of energy that’s transmitted over time – in this case, to heat the brakes) to bring the car from 70 km/h to 0 km/h is identical to the amount of power it takes to bring the same car from 100 km/h to 70 km/h. (An audio geek might joke that 70 km/h is 3 dB slower than 100 km/h.)

The conclusion

Slow down. You’re not going to make it to the meeting anyway, and driving a little bit faster means you’re going to hit the train much harder than you think.

Q stands for…

These days, I’m spending a lot of time wrapping my head around the relationship between the frequency and the time responses of filters. In doing so, I’m digging into the concept of “Q”, of course. As a result, I’m reading my old books and some Internet sites, and I’m frequently presented with something like the following:

That, of course, is from the Wikipedia entry on “Q”.

However, in the Bell Telephone System Technical Publication – Monograph 2491, called “The Story of Q” by Estill I. Green ( published in the American Scientist, Vol 43, pp 584-594, in October 1955), it states:

“For a time, Johnson* designated the ratio of reactance to effective resistance of a coil by the symbol K. It was in 1920, while working the practical application of the wave filter which G. A. Campbell had invented some years before, that he for the first time employed the symbol Q for his parameter. His reason for choosing Q was quite simple. He says that it did not stand for ‘quality factor’ or anything else, but since the other letters of the alphabet had already been pre-empted for other purposes, Q was all he had left.”

So, if we’re going to be pedantic (which I love to be) there are two errors on that Wikipedia page. Firstly, Q does not stand for Quality. Secondly, it’s not the “Q factor”, it’s just the “Q”.

As an aside, that monograph is not only informative, it’s fun to read (depending, of course, on your definition of “fun”). For example, near the end of the paper, Green applies Q to rotating bodies (which is not a surprise, since an audio-wave oscillation is just a rotation represented in two dimensions). In that section, he points out that the rotation of the earth is slowing down due, in part, to tidal friction. Consequently, the length of a day is increasing at a rate of 0.00164 second per century, which would make the Q of the rotation of the earth equal to about 10,000,000,000,000 (10^13).

* K.S. Johnson worked in the Western Electric Company’s Engineering Department, which became Bell Telephone Laboratories in 1925.