Messing around with Sound

In fairness to you dear reader, I ought to open with a confession: this post contains many more words than I’d usually aim for. In order to mitigate this I have moved several hundred words to an [endnotes] section so you only need read them if you’d like a little more detail/information. I’ve told myself that it may prove useful for anyone else thinking of giving a talk to a lay audience on the same topic; who knows. In addition there are, sadly, few pretty pictures to soften the blow, but I have added lots of links to animations and the like …

For the first three years of my retirement – from academic life that is, I was a scientist before that, and I still am – I led three two-hour sessions, one per week, on the art and science of glass for my local University of the Third Age (U3A) branch. (It has over 1000 members, making it one of the larger branches on the UK scene; the web site is here to which I contribute the odd snippet now and again, here.) It was huge fun, due in no small part to my audiences of smart and careful listeners. In the process, I got the opportunity to develop further whatever skills I had in conveying aspects of science without the use of mathematics. However, after the 2018/19 season I decided to set this material to one side for a while. We all need new challenges from time to time, when the old must make way for the new. I had by this time developed a session on the topic of ‘Radiation’. This was a start, but my plan, such as it was, involved introducing new topics on a rolling basis. Accordingly, in the following year, I successfully trialled a session which explored the question: ‘What’s so special about the Earth?’. After that – and we’re now into the current, 2019/20, season – came sessions on ‘Colour’ and on ‘Sound’. Where I go from here is undecided [i], although it’s definitely time to lay ‘Radiation’ to one side for a while as everyone who wants to learn something under this heading has by now been able to. (I know this because, unlike my other sessions, there wasn’t a waiting list of ‘reserves’ hoping to get a seat on the basis of a last-minute drop-out.)

All of this is but a preamble to the central reason for writing a blog post after a relatively long hiatus. Put simply, I promised to draft something on the topic of ‘Sound’ [ii] in the hope that it would act as a sort of memento for those brave souls who risked contracting my cold virus in order to participate in the session on January 7th. (And participate they did by the way: every bit as sharp-witted and engaged as any other U3A group I’ve encountered, and with a great sense of humour – more of that later …) 

As a bit of fun, whilst I was busying myself setting out the various bits of kit I’d borrowed [iii] for the event, I projected onto a large TV monitor the live ‘oscilloscope’ trace [iv] of the sounds present in the venue as people arrived and settled down to chat to each other. It was fun to see the realisation dawn that it was they who were creating the changing ‘squiggles’ on the screen. (The screenshot shown in the figure above was not captured at the time but specifically for this post – it’s derived from a piece of music I played for the purpose – but the principle holds.) This pre-session bit of ‘show and tell’, which I explained to everyone later on, worked particularly well because we were in a relatively small room with hard walls and large windows bouncing the sound around. Unfortunately, this would make life less easy for later demonstration experiments. A partial solution involved dropping the wood-slatted venetian window blinds and angling the slats in the hope that any echoes would be broken up a little. It worked tolerably well. Even with the same slides and associated ‘show & tell’ kit, no two talks are ever the same; it’s part of the fun of the whole process.

Sound was of course listed in the relatively short Science section of our U3A programme of events for the year – science-related topics represent about 10% of the total – so we started with a bit of basic terminology and a few definitions in order to get the ball rolling. A key concept was that of an oscillation: a repeated to and fro motion. All waves are oscillations. (Hence, a ‘Mexican wave’ is not actually a wave at all – it’s a pulse.) Having got that under our belts it was possible to focus on sound waves and to illustrate what was going on by considering the to and fro motion of air molecules in front of a loudspeaker cone. As the cone moves forwards it compresses the air in front of it (i.e. increases the pressure) and as it moves back again it causes the air pressure near it to decrease; the air molecules are oscillating backwards and forwards. In colliding with the next layer of air molecules this oscillation is propagated outwards; all the while, individual air molecules are simply oscillating forward and backward, forward and backward. The animation shown here illustrates the behaviour quite well. Of course, sound travels in liquids and solids as well; the same generic principles pertain, but the atoms/molecules are closer together and tend to be bonded to one another far more strongly than is the case for air molecules. The speed of sound in dry air at 20ºC is 343 m/s (at 0ºC this drops to 331 m/s [v]; humidity also has a significant effect) but in helium gas it’s a whopping 965 m/s, which is why one’s voice sounds high-pitched after inhaling helium. The speed goes up again in water (for seawater it’s about 1522 m/s) and leaps up again in solids to several thousands of metres per second. As a passing observation, the variation in the speed of sound through different materials is what enables geologists and geophysicists to use the technique of seismology to such good effect – but to explore that would require another blog post.

We looked at what was meant by sound frequency – the note or pitch – and then at the difference between intensity and loudness, the latter being the subjective response of our ears and brain to changes in the intensity of sound waves arriving at our eardrums. This enabled us to get to grips with the oft-quoted unit of the decibel as a measure of loudness. It was also a great point at which to reflect on what an amazing instrument the ear actually is: capable of detecting frequencies from a few tens of oscillations per second (one oscillation/s is called a Hertz, Hz) to around 18,000 Hz, and able to do so over twelve orders of magnitude in intensity [vi]. Interestingly, a baby’s cry is at a higher frequency than an adult’s, about 500 Hz compared to ~350 Hz, which corresponds much more closely to the frequency range at which an adult’s hearing is most sensitive. The obvious experiment was to use one of my borrowed signal generators to send sound waves of a particular frequency from a loudspeaker and to vary the frequency in order to determine the range enjoyed by those present. No-one got much below 40 Hz or, with a couple of exceptions, higher than about 14,000 Hz; our ears degrade with age.

There are sounds we will never hear of course. At high (ultrasonic) frequencies we know that bats are able to echo-locate their food, and in the medical world we design instruments to image parts of the body, break up unwanted lumps and so on. At the other end of the scale, low (infrasonic) frequencies are associated with elephant and whale calls as well as with the blades of wind power turbines. There are occasions when the frequency (or equivalently the note or pitch) of a sound seems to change all by itself. It’s most obvious when an emergency vehicle is travelling towards you and then passes by and travels away: the frequency seems higher on its approach and then drops as it travels away. This is an example of the Doppler Effect (see animation here). It was demonstrated in a simple but quite dramatic way by fixing a small speaker (from a printed circuit board) to a battery via a switch and twirling the whole thing above my head in a circle. The frequency (pitch) of the sound as heard by my lovely audience increased or decreased depending on whether the source was approaching or receding from them.

Our next keyword was ‘superposition’. Although an extremely important principle across Physics, it has particular ramifications in the context of sound waves. Basically, we can think of overlapping sound waves as adding together in a very simplistic manner: if an increased pressure bit of one overlaps an increased pressure bit of another, the result will be an even higher pressure; if an increased pressure section of the wave were to overlap with a reduced pressure section of another however, they would tend to cancel one another out. This may be illustrated in practice in several ways, but I started with beats. This occurs when we hear two sound waves which differ slightly in terms of frequency – usually by less than 10 Hz: we end up hearing only one frequency, which is the average of the two, and its intensity goes up and down. Twin-propeller aircraft are famous for giving rise to this effect. In our case, I was able to demonstrate the effect by running two loudspeakers from separate signal generators and then slowly varying the frequency of one of them so that it approached and went past the frequency of the other. This set of animations may help.

We then came to a really fun bit, when I got everyone to stick a finger in one ear, stand up, bob down and move around the room. It was quite a sight. We were talking about the creation of an interference pattern using my two loudspeakers, but this time powered from a single signal generator to ensure that they were perfectly matched. It’s a tricky concept, but this animation reveals the essence of what we created, in 3D, using two sound waves. What we established was a stable room-filling pattern of high and low intensity sound through which we might move. I chose a frequency in the region of 1500 Hz for this simply because I knew it would provide a pattern spacing of less than half a metre. Why the need to block one ear (or remove one hearing aid in a couple of cases)? So that we could explore the sound interference pattern without the confusion of having two ‘detectors’, our ears, send separate signals to our brains. After a few minutes of fun, and a bit of discussion on whether one could navigate around the room by counting the number of high/low intensity regions we had moved through, I asked everyone to park themselves at a low intensity point. If we were experiencing what I had told everyone we were, then by unplugging one of the loudspeakers the sound intensity at their ear – their sound detection device – ought to go up. Thankfully, everyone was able to confirm to me that it did. 

Resonance was to be my final topic. Although we were able to cover the basics – the necessity to ‘drive’ the system at its natural frequency – we ran out of time before I could set up the coup de grace: smashing a wine glass using only sound. My laptop’s soundcard scope came to fore again in that I could at least show everyone how to find the natural/resonant frequency of a wine glass simply by flicking its edge with a fingernail. The screenshot of one I had tried at home is shown above: the glass rings at a particular frequency/note. In this case – indeed, for all the odd wine glasses I possessed – the natural, or resonant frequency was in the region 870 Hz. Subject the glass to a high enough intensity of sound at that same frequency will cause it to vibrate more and more … until it breaks. This video shows precisely the arrangement I had intended to use.

From the questions posed at the time and from subsequent kind and generous feedback I’m clear that were there more time, those present would also have enjoyed to hear about why musical instruments sound so different even whilst playing the same note, including what makes a standing wave. Perhaps next time. All I could leave them with as our session came to its end was a warning and a piece of prose:

• beware sounds at 5-7 Hz as this corresponds to the resonant frequency of our body’s water-filled cavities (- an important consideration when designing car suspension systems, and otherwise) and
• enjoy George Eliot’s appreciation of resonance: “How will you know the pitch of that great bell too large for you to stir? Let but a flute play ’neath the fine-mixed metal: listen close ’till the right note flows forth, a silvery rill: then shall the huge bell tremble – then the mass with myriad waves concurrent shall respond in low soft unison.” (Middlemarch, OUP, Oxford).

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Endnotes:

[i]  Is there scope for something on waves, or on quantum mechanics? What about an open Q&A session: could I pull together a sufficiently multi-disciplinary team who would volunteer to join me in the ‘bull pit’, and would there be an audience? Ought I to step sideways out of the U3A and into something qualitatively new? There are lots of possibilities, but as yet no decisions. 

[ii]  Indeed, there are blog posts on each of the topics I’ve covered within the U3A thus far with the sole exception of ‘Sound’, so it’s surely got to happen. Existing posts may be found by clicking on the following links: Radiation (here), Earth (here), Colour (here and links therein); Glass is at the heart of half the posts on my blog, so take you pick (e.g. here or here; or if you’d like to peek into my professional interests in glassy materials, try here). 

[iii] I am immensely grateful to my old department (The School of Physical Sciences, University of Kent) for their continued support in my science communication endeavours, and in particular to ex-colleagues Dr. Dave Pickup and Dr. Vicky Mason. I made sure to acknowledge this support in my talk, as is my habit whenever I use borrowed items for ‘show-and-tell’. 

[iv]  I used a piece of software which is freely available to download for use within non-commercial/educational contexts (here). It uses the laptop’s soundcard, so it does have limitations of course; however, it is extremely useful for talks such as this one.

[v]  I’ll not cover it here, but this is the reason why sound carries further at night. The cooler air near the ground has the effect of refracting (bending) the sound waves downward – thus, the sound wave’s energy is not dissipated up into the atmosphere quite so much. In the daytime, when the air near the sun-bathed ground is warmer, the waves are bent upward and thus away.

[vi]  From 1 W/m² to 1 pW/m² where W, the Watt, is a measure of the wave’s energy and a picoWatt is one million millionth of a Watt. For context/comparison: the heat output from a single adult is in the region of 100 W; a domestic electric kettle typically consumes power at a rate of 2,000-3,000 W. The ear is thus a very sensitive wave detector.