Citizen Science #19 by Jamie Zvirzdin

Energy Demystified: Understanding Sound Energy

The intense hum of a singing bowl reverberated through the quiet yoga studio, filling the space with an almost otherworldly sound. For many, this practice brings peace and mindfulness. But for me and my mother-in-law, Catherine, the experience was quite different. As our yoga teacher circled the mallet around the edge of the bowl, we both felt a sharp discomfort, a painful resonance.

Wincing, I covered my ears, as I do when ambulances pass. I didn’t feel I could interrupt or leave, which might be considered rude, so I endured it as best I could with my ears covered. As class concluded, I asked the yoga teacher why the sound hurt my ears, and she said it was because my sexual chakra was off-balance.

This was laughably far from true, and it rather astonished me that she’d say this in front of the whole class, but the mystery remained: Why did Catherine and I feel physical pain at this sound when others liked it?

How Sound Energy Is Produced

So what’s going on with singing bowls? When the suede mallet is rubbed around the rim of the singing bowl, the friction of this action is not uniform, but “stick-slips”: Essentially, the mallet grabs the bowl’s metal surface, then slips, then grabs again, repeating this cycle rapidly. Every time the mallet sticks, it actually deforms the metal very slightly, on the microscopic scale. These small deformations store elastic potential energy (remember Citizen Science article No. 17?) in the metal.

Then, when the mallet slips, this stored energy is released as kinetic energy (see Citizen Science article No. 15) in the form of vibrations. The vibrations then emanate through the bowl at a fundamental frequency, but as they do, the shape of the bowl amplifies the sound, producing resonance. Curiously, this same stick-slip friction phenomenon also happens with screeching chalk, squealing brakes and squeaky shoes on a basketball court. All these vibrations have measurable energy.

How Sound Energy Is Measured

Whether it’s a screech, a squeal, a squeak, or a much more pleasant sound—a violin bow rubbing across a string is another stick-slip example—sound energy is a form of mechanical energy that travels through a medium (usually air, water or solid objects) as a wave. Sound waves push and pull air molecules, creating areas of high pressure (compression, where the air molecules are close together) and low pressure (rarefaction, where the air molecules are spread apart). Imagine this invisible, undulating movement propagating from the bowl through the air toward you at a certain speed (the speed of sound in air at room temperature is 346 meters per second!) until it reaches your ears, where it is interpreted as sound when the waves stimulate nerves, which then send electrical signals to the brain in a fascinating and complicated way.

Sound energy can be measured in Joules, just like all the other energies we’ve talked about this year. For sound, however, it’s more practical to see how that wave energy moves through space and time—think of sound waves from a singing bowl spreading through the yoga studio space over a period of time. When we account for those extra factors that affect how we perceive the sound, we call this sound intensity, which is the power per unit area carried by a sound wave. We measure sound intensity in decibels (dB), a logarithmic scale that gives us the comparative intensity or loudness of a sound.

For example, if you’re in a quiet office with some mild background noise, that’s about 30–40 dB. If you’re sitting a few meters from gentle waves lapping on the beach, that’s about 50–70 dB. If you’re on a boat in a terrible tempest with waves crashing all around you and the captain is screaming at you to abandon ship, that’s about 90–120 dB. I estimate that the singing bowl I heard was between 70 and 90 dB, which is usually considered a safe level for short-term exposure. Usually.

The frequency of a sound refers to the number of cycles (vibrations or waves) that occur in one second. Think of a wave crashing on the beach: it crests, then crashes, then draws back. That is one full cycle. We measure frequency in units of Hertz, abbreviated Hz and named after Heinrich Hertz, a German physicist. For a visual comparison, the average ocean wave crashes on the beach at a frequency of 6 to 12 waves per minute, which is equivalent to 0.1 to 0.2 waves per second (even though this makes less sense visually). We can now say that the average frequency of a physical wave crashing on a beach is about 0.1 to 0.2 Hertz (Hz).

With sound waves, the frequency of the vibration determines the pitch of the sound. We humans can typically hear sounds ranging from 20 Hz to 20,000 Hz (an enormous range). The sound of waves crashing on the beach, for example, has a broad frequency range, typically between 100 Hz and 1,000 Hz. This range includes a mix of lower frequencies that give the sound its deep, rumbling quality, as well as higher frequencies that add the splashing and crashing details. This soothing mix of frequencies is why we like to go to the beach and why we often use the sound of waves as white noise if we have trouble sleeping.

However, sometimes the frequency can make the sound seem louder. The human ear is naturally sensitive to frequencies between 2,000 Hz and 5,000 Hz because of the length of the ear canal (around 2.5 cm, about an inch long). Hence bird chirps, alarm clock alerts and other electronic noises, baby cries, buzzing mosquitoes, high-pitched music notes, and some human speech sounds (like the “s” and “t” sounds) can seem particularly loud to us even if they have a low decibel level.

How Sound Energy Is Enriched

Here’s where things get particularly interesting. Musical instruments, voices, even wind, trees, and machines, can resonate at a fundamental frequency, which varies according to shape, material, and other characteristics. When the vibrations repeat, the next round of waves can amplify the first round of waves, creating higher frequencies known as harmonics and overtones (they’re defined slightly differently but they are similar in nature). Sounding an A-note on a violin, for example, gives us a fundamental frequency of 440 Hz, but then additional harmonics at 880 Hz, 1320 Hz, and so on join the sound. This gives the sound its timbre, its particular tone quality.

A typical singing bowl, therefore, might produce a fundamental frequency between about 100 Hz and 500 Hz (the bigger the bowl, the lower the starting frequency), with harmonics and overtones reaching right up into that sensitive 2,000 to 5,000 Hz range. If the sound echoes in an enclosed room like a yoga studio, even more overtones could drive up the frequency.

I don’t know if it was the material, the shape, the loudness, the pitch, or any echoing overtones from the singing bowl that day that caused Catherine and me to feel pain, but I do know that humans can experience hyperacusis, an increased sensitivity to sound. Hyperacusis has been reported by a variety of people with conditions like multiple sclerosis, post-traumatic stress disorder, anxiety, depression, Lyme disease, migraines, autism, ADHD, severe head trauma and more.

I have never been fully tested, but I suspect I have some level of ASD or ADHD (or both), as it runs in my family. I have a problem with all of the sounds I mentioned in the 2,000 to 5,000 Hz range, particularly if they are repeated. In March of 2012, Catherine was hit on the side of the head with a heavy backpack by a special-needs student, which knocked her into a storage cubby. She experienced a traumatic brain injury that took her years to come back from. She was incredibly sensitive to sound—clocks ticking, birds singing, large groups of people all talking all drove her bananas. Yoga teachers can be more aware of conditions like hyperacusis among their participants, and we can all manage our acoustical environment for our greater health and happiness.

Listening to singing bowls, it turns out, is a relatively modern phenomenon, starting in the United States around the 1970s. Since then, the benefits of singing bowl therapies are still debated. In a review of studies involving how singing bowls affect human health, researchers Stanhope and Winstein said, “Given there were few studies and the potential risk of methodological bias, we cannot recommend singing bowl therapies at this stage” (“Complementary Therapies in Medicine Journal,” 2020).

Even if I choose the sound of mild ocean waves over singing bowls, I marvel at the interesting, powerful, and measurable sound energy these stick-slippery bowls produce, as well as the range and complexity of the human auditory system.

Jamie Zvirzdin researches cosmic rays with the Telescope Array Project, teaches science writing at Johns Hopkins University and is the author of “Subatomic Writing.”