Waves by Design: Instruments, Concert Halls, Headphones and Wave Energy

Engineers who think in waves

Why does a guitar have a hollow body? Why do concert halls have strange bumpy panels on the walls? How do noise-cancelling headphones make an airplane cabin almost silent? Every one of these is a design built on the wave physics you have learned in this unit: standing waves, resonance, reflection, absorption and interference. In this lesson you will look at designs through a physicist's eyes and practise assessing a wave technology.

Musical instruments

Every instrument has three parts: something that vibrates, a way to choose the frequency, and something that resonates to make the sound louder.

• Strings (guitar, violin, fiddle, piano): the fundamental is f₁ = v/(2L). Players change L with their fingers; tuning pegs change the tension (and so v). A thin string vibrating alone moves very little air, so the vibration is passed to a wooden soundboard or hollow body that resonates and pushes much more air. The fiddle is central to Métis music, and its sound comes from exactly this string-plus-body design.
• Wind instruments (flute, clarinet, trumpet, pipe organ): an air column resonates. Opening finger holes effectively shortens the air column, raising the pitch. A flute behaves like a pipe open at both ends; a clarinet behaves roughly like a pipe closed at one end, so it can play lower notes for its length.
• Percussion (drums, xylophones): a stretched membrane or a bar vibrates. Many First Nations communities make and play hand drums and larger drums; the Inuit qilaut is a frame drum with a skin stretched over a hoop, held by a handle and struck on the frame with a beater. A tighter or smaller drum head vibrates at a higher frequency.

The timbre of an instrument comes from which harmonics are present and how strong each one is.

Concert halls and classrooms

A good room for music or speech balances three things:

• Direct sound reaches every listener clearly. Sloped seating keeps heads from blocking it.
• Early reflections from the ceiling and side walls arrive a few hundredths of a second after the direct sound and make music sound full and loud. If a reflection arrives too late (more than roughly 0.05 s to 0.1 s after the direct sound), it is heard as a separate, annoying echo.
• Reverberation should suit the room's use: roughly 2 s suits a symphony orchestra, while classrooms and lecture halls need much less (under about 1 s) so that speech stays clear.

Designers control these with shape (angled ceiling panels aim reflections at the audience; concave walls that focus sound are avoided), absorbing materials (curtains, padded seats, fabric panels, acoustic ceiling tiles) and diffusers that scatter sound evenly so there are no loud and quiet spots from interference. Padded seats are designed to absorb about as much sound as a seated person, so rehearsals in an empty hall sound like concerts.

Headphones and hearing protection

• Passive isolation: closed earcups and well-fitting ear tips block and absorb sound, especially high frequencies.
• Active noise cancellation (ANC): a small microphone picks up incoming noise, a chip creates an inverted copy (half a cycle out of phase), and the speaker plays it together with your music. The noise and anti-noise interfere destructively. ANC works best on steady, low-frequency sound like engine hum, because the electronics can keep up with slow, predictable waves.
• Safe listening: quieter surroundings mean you can keep the volume lower, which protects your hearing (see the lesson on decibels).

Case study: wave-energy buoys

Ocean waves carry a lot of energy, and the power of a wave grows with the square of its amplitude and with its period. A point-absorber buoy floats on the surface and is anchored to the sea floor. As waves lift and drop the buoy, a generator inside turns that up-and-down motion into electricity, which travels to shore through an undersea cable.

To assess this technology, consider:

• Benefits: renewable, no fuel and no greenhouse-gas emissions while running; waves are more predictable than wind days ahead; buoys are low on the horizon.
• Challenges: storms can produce waves many times larger than normal (energy ∝ A²), so buoys must survive huge forces; salt water corrodes equipment; maintenance at sea is expensive; buoys and cables may affect fish, marine mammals, fishing and shipping routes.
• Questions to ask: How much electricity does it produce compared with its cost? What is its lifetime? Who was consulted, including coastal and Indigenous communities whose waters, rights and livelihoods may be affected?