Musical instruments and resonance

I’ve started a project exploring musical instruments and the physics controlling their audio properties. Mostly I’m interested in brass instruments like a trumpet or trombone‒instruments that are tubular for much of their length. Brass instruments have a constant diameter at their beginning. As the tube approaches the end, the instruments become more conical until terminating in a flared bell. I chose them because I played the trumpet in high school. It’s familiar.

One book that I’m using to help understand what is happening is “The Physics of Musical Instruments, 2nd edition” by Neville H. Fletcher and Thomas D. Rossing. It has quantitative descriptions of the properties of real instruments.

One interesting idea is to consider brass instruments as “reed instruments.” For a brass instrument, the “reed” is the lips of the performer. This allows brass instruments to use the same equations as woodwinds. As a first approximation, lips and reeds have similar properties of interrupted air flow. It does make a difference whether the opening closes with increasing pressure or opens with increasing pressure so the analogy has its limits.

My first experiments have been with a pipe resonating at different frequencies. My method of creating data is to input a sweeping pitched sound to one end of a pipe with a speaker. The pipe resonates at different frequencies so that the intensity of the sound so the other end varies over time. This is a example configuration with headphones presenting the sound on the right end and a microphone picking up sound on the left. I haven’t calibrated the frequency response curve of the microphone and speakers.

For example, when I sweep the input sine wave from 50 Hz to 2000 Hz over 2 minutes on one end of a 1m 1/2″ PVC tube, the amplitude from the other end creates this graph. I measure the amplitude as rms (root mean square) by squaring the values of each sample in a block and then taking their average. This helps in comparing one block to the next.

time vs. amplitude

One thing I notice with such examples is that as the frequency goes up, there is more and more noise in the wave form. The shapes become more ragged. It should be easy to identify the time of the different peaks and thus their frequency but this and other sources of noise interfere.

If I take above run and make an image of its frequency distribution, I get this. The Y axis isn’t calibrated, but starts at 0Hz at the bottom. This chart has the whole duration of a single observation session. The graph above is trimmed to exclude the times that I wasn’t activating the system.

Time vs. frequency

An interesting feature of the graph are the higher overtones from the input sweep. They show up as lines with higher slopes than the main output. This example, I can see 4 extra lines, but different configurations of microphone and pipe may show only one or two. (The third overtone is barely visible above the middle of the run.) Also, if I look closely, I see very faint equispaced horizontal lines. I suspect that those are from my computer fan but I haven’t verified it.

The gray noise at the bottom of the graph are different noises from within my house. I haven’t identified the causes of those or their frequency. Some of the graph is marked with mechanical bumps that show up as lines starting at zero hertz. The vertical features centered on the main input frequency are a common feature of these charts. I’m not sure whether they are real or are an artifact of my processing.

(This representation doesn’t help me identify the position of the peaks.)

An interesting adjustment is needed when I break the signal into chunks. For the Fourier transform or other analyses, I need to block the chunks so that they end at the zero crossings of the input waveform. I pick a minimum number of samples for a block and then search further for the next positively sloped zero crossing. If I don’t do that, the sharp edges at the ends of a block add artifacts that hide real effects. The software I’m using for FFT, FFTW allows me to have non-power-of-two long blocks which is essential for seeing useful results.

Who do I see in the mirror?

One way to understand a complex system is to locate its holes and find what normally fills them. The brain is a system like that and one way of identifying functions of the brain is to describe deficits.

Examples include aphantasia and face blindness. Aphantasia refers to the inability to form visualizations in ones imagination. Face blindness (prosopagnosia) describes the inability to recognize faces. There are many other deficits, each with a different set of symptoms.

The change in capability could be due to a malfunctioning part of the brain or a disruption in the connection between areas. Perhaps an injury or disorder has damaged part, pointing toward the purpose of that region. Sometimes the affected area of the brain is well understood.

For me, I can recognize people really easily. It doesn’t take me looking at a person ‘s face to identify them. The face is an easy point of access to knowing who a person is. However, looking at a person from behind is often enough for me to know who I’m approaching.

The hole that puzzles me is the difficulty of recognizing myself. I can see photos of me or look at myself in a mirror. I don’t think that it is someone else, but rather it’s a conscious act to recognize that it is me. Old pictures or new, none of them look like “me.” I just don’t feel the same connection to myself that I do with other people.

It seems that this would be something a psychoanalyst might have comments on, but therapists and psychiatrists don’t hear anything alarming in this. It’s more “That’s interesting.”

There isn’t a strong emotional impact on me with the issue, just that it seems atypical of how most people react to their picture. I don’t know.

I can recognize you, but I can’t recognize me.

Gasoline and a Polyester Suit

I was putting away my laundry and realized how little I know about my clothes. It’s a wide span of ignorance covering something I interact with every day. Like my superficial knowledge of transportation, I trust the experts who make high quality garments to know how to create them.

A first level of ignorance involves the fabrics that clothes are made from. Dacron, cotton, linen, polyester, and wool just start the list of fibers. My list is short and shallow. I know some of them are natural, made from plants or animals. Others are synthetic, usually polymers, and are a recent invention. I know fabrics can be made from a combination of these substances. Some shrink when they are washed, others can be damaged in a clothes dryer set too hot.

What started me reminiscing on this began when I was looking at my laundry and wondering “Who designed this garment?” “How was it manufactured?” “What attributes were the designers considering?” “What is the science behind the little differences from one garment to the next?” “Who did the labor to put it together?” “What steps were automated?”

My cousin made a dress in the style of Jane Austen’s time. I also have the tools to make my own shirts, but don’t have the skills to be successful. I’d like to be better able to use my sewing machine, but I haven’t put in the effort. I’ve got thread and know where I can buy yards of cloth, find a pattern, and even get training. The whole exercise isn’t about the economics of clothing but rather the satisfaction of developing a new skill and making something to demonstrate that I have done so.

My Grandmother was skilled at crochet. My sisters, cousins and I have afghans that she made. It is a nice memento to keep her in my mind. The issues involved with those blankets are lost on me but it is a reminder of her love.

Transportation, I start by saying I don’t know the chemistry of gasoline and how it is manufactured. Next, I only have a cursory understanding of the physics behind the internal combustion energy. My vehicle seems like a straightforward object even though I know that it is not. Part metal, part plastic, it does the work to turn the wheels and follow my steering, but I don’t really understand the how and why. A simple example is that I can’t repair a door latch nor explain its mechanical principles.

In another facet of transportation, my knowledge of how roads are made, is mainly gleaned from watching construction teams working on a highway as I drive past–that’s horribly superficial. I know that there are inspections and standards for roads. The purpose of those regulations are to make roads reliable. I don’t see the calculations made in the design of bridges, but I do drive on them.

One of my shirts shows a simple design change that is evidence of its designer’s intervention. The bottom buttonholes of some of my button down shirts have a horizontal opening instead of the vertical buttonhole of the rest. That makes sense to me because it helps prevent the bottom button from popping open. Just as the top button is almost universally horizontal, these horizontal bottom holes were an insight by its clothing engineers. This gives me a a tiny window into the process of design and manufacture.

There’s so much I take for granted that someone else has expertise in. I don’t begrudge those experts and am glad when my car gets me home and my seams don’t rip.

It’s foolish to attack scientists and experts who use their expertise and advanced knowledge. Just because I don’t understand some point of that knowledge, doesn’t validate my rejection of it. Although I can wonder and try to learn more, I don’t reject them as “elites” and deny their science.

Worse than rejection is to impugn bad faith on professionals through conspiracy theories and denial of their commitment to ethical principles. One friend reminds me if you spot it, you got it. Shadowy accusations of bad faith and conspiracy are actually an indictment of their accuser’s bad faith, not a sign of insight, wisdom or superiority.