Trombone

Module VIII

In the Classroom

Play the real horn in front of a class while the screen measures it. Ready-made demonstrations for maths and science, ages 11–18.

1.Set up (two minutes)

Laptop on the projector, within a couple of metres of you. Open this page, press Start the microphone and allow it. Set B♭/F or straight B♭ in the header to match your instrument.

2.Play, then ask

Each card says what to play, what the class should look at, and the questions to ask before you explain. Keep the Reveal folded until they have guessed.

3.Let them measure

Use Capture to log one note per slide position. The class’s own numbers make the graph — predictions, error and all.

live lab · play the real trombone

The screen measures the horn

note (sounding)

—

play a long note

frequency

—

vibrations per second (Hz)

period

—

milliseconds per vibration

wavelength

—

metres · λ = v ÷ f, v = 343 m/s

harmonic no. (position 1)

—

pick the tube below

the sound, measured (louder = higher)1×, 2×, 3×… the note’s frequency

the tube you’re playing

Position 1: lowest possible note (the pedal) ≈ 58.3 Hz. Every note you can play here is a whole-number multiple of it.

Try: one harmonic — the F on the fourth line of the bass staff in 1st, then down through positions 1→7 without changing your lips — capturing each. The prediction is ÷ 1.0595 per position.

Captured notes appear here as a graph: measured (dots) against the prediction (line).

the run-sheet

8 demonstrations with the real trombone

  1. 1.What is actually vibrating?

    ages 11–14 · 8 min
    vibrationfrequencyresonance
    play
    Buzz your lips alone. Buzz into the mouthpiece alone. Then put the mouthpiece in the horn and play a long B♭ in 1st position (the B♭ in the middle of the bass staff).
    show
    Live lab — spectrum and big numbers (above)
    ask
    1. Which of the three sounded most like a note? Why?
    2. The screen says about 117 Hz. What is happening 117 times every second?
    3. If the lips make the buzz, what is the long tube for?
    Reveal — the science

    The lips are a valve, opening and closing about 117 times a second. On their own they buzz at whatever speed they like — a messy spectrum. In the horn, the air column has a few frequencies it 'likes' (resonances) and it pushes back on the lips until they lock to one of them. The spectrum turns into clean, evenly spaced spikes.

    frequency = vibrations per second. B♭ ≈ 116.5 Hz → one vibration every 1 ÷ 116.5 = 8.6 milliseconds.

    Sound as vibration; frequency and pitch (NCERT/CBSE Class 8–9 ‘Sound’; NGSS MS-PS4-1).

  2. 2.One tube, many notes: the harmonic series

    ages 11–18 · 10 min
    multiplesratiosequences
    play
    Stay in 1st position the whole time. Lip-slur up: low B♭, F, B♭, D, F (the bugle notes). Hold each for three seconds.
    ask
    1. The slide never moved. How did the note change?
    2. Read the frequencies off the screen. Do you see a pattern?
    3. Why can’t I play every note without moving the slide?
    Reveal — the science

    A tube of fixed length can only resonate at whole-number multiples of its lowest frequency (the pedal B♭, 58.3 Hz). The notes you can lip-slur to are the 2nd, 3rd, 4th, 5th and 6th of those multiples — the harmonic series. The gaps between them are big at the bottom and close up at the top, so there are notes in between that this length of tube simply cannot make. That is what the slide is for.

    58.3 × 2, 3, 4, 5, 6 = 116.5, 174.8, 233.1, 291.4, 349.6 Hz. Ratios 2 : 3 : 4 : 5 : 6. Octave = 2 : 1, fifth = 3 : 2, fourth = 4 : 3.

    Multiples and ratio (CCSS 6.RP.A.1); sequences; harmonics (HS physics: standing waves in pipes).

  3. 3.Longer tube, lower note — measured

    ages 13–18 · 12 min
    inverse proportionreciprocal graphdata
    play
    Pick one harmonic — the F on the fourth line of the bass staff, in 1st position — and keep the same lip setting while you move down 1 → 7: F, E, E♭, D, D♭, C, B. Capture each note in the live lab.
    show
    Live lab data logger (capture one note per position) (above)
    ask
    1. Predict before each capture: higher or lower? By how much?
    2. Look at the last column. What stays the same while the slide moves?
    3. If I could make the tube twice as long, what would the note do?
    Reveal — the science

    Sound travels at a fixed speed in the room. The tube length sets the wavelength, so frequency = speed ÷ wavelength falls as the tube grows. Double the length, halve the frequency: frequency × length is a constant. The graph is not a straight line — it is the reciprocal curve.

    f × L = constant ⇒ f = k ÷ L. On harmonic 3 at 20 °C, f × L for the whole air column ≈ 1.5 × 343 ≈ 515 Hz·m.

    Inverse proportion and non-linear functions (CCSS 8.F.A.3); v = fλ (NGSS HS-PS4-1).

  4. 4.Why the positions get further apart

    ages 14–18 · 10 min
    exponential growthgeometric sequencerational exponents
    play
    Put masking tape on the slide and have a student mark where your hand is for positions 1–7 while you play a slow chromatic scale down from B♭. Measure the gaps with a ruler.
    ask
    1. Every position is one semitone. So why are the gaps different?
    2. Is each gap a fixed number of centimetres longer, or a fixed percentage longer?
    3. Where would an 8th position be?
    Reveal — the science

    One semitone lower always means the whole tube × 1.0595 (the twelfth root of 2). The tube is longer each time, so 5.95% of it is a slightly longer piece each time: the gaps grow from about 8.1 cm to 10.9 cm. Equal ratios, not equal steps — that is exponential growth.

    L(n) = L₀ × 2^((n−1)/12). Gap from 1st to 2nd = 2.74 m × 0.0595 ÷ 2 ≈ 8.1 cm (÷2 because the slide is a U: moving it 1 cm adds 2 cm of tube).

    Linear vs exponential (CCSS HSF-LE.A.1); rational exponents, 2^(1/12) (CCSS HSN-RN.A.1).

  5. 5.The thumb trigger: a fourth is four-thirds

    ages 12–18 · 8 min
    ratioscale factorapproximation
    play
    Play C (2nd space of the bass staff) in 6th position, then the same C with the trigger in 1st position. Then play the low E below the staff in 7th and keep going down with the trigger: E♭, D, D♭, C … and try for B.
    ask
    1. The same note in two places — what did the thumb change?
    2. If the tube is 4/3 as long, how far apart will the trigger positions be?
    3. Why can’t I reach low B with the trigger down?
    Reveal — the science

    The trigger switches in about 0.92 m of extra tubing, making the horn 1.335 times longer — a perfect fourth lower. Because every trigger semitone needs 1.335 times as much slide, the positions spread out: only six fit, and the seventh (low B) would be 75.7 cm out, past the end of the slide.

    2^(5/12) = 1.3348 ≈ 4/3 = 1.3333. B♭ 7th = 56.7 cm × 1.335 = 75.7 cm. Tenor slide ends near 64 cm.

    Ratio, scale factor and percentage increase; approximation.

  6. 6.Warm air, sharp horn: the speed of sound

    ages 13–18 · 6 min
    speed of soundtemperaturepercentage change
    play
    Play a long B♭ with the horn as it is and note the reading. Breathe warm air through it for 20 seconds (no buzz) and play again.
    show
    Live lab — change the temperature box and watch the wavelength (above)
    ask
    1. Why do brass players blow warm air through before they tune?
    2. The tube didn’t change length. What did?
    3. Is a brass band flat or sharp on a cold morning?
    Reveal — the science

    Sound travels faster in warm air. The tube fixes the wavelength, so if the speed goes up the frequency must go up too: the horn goes sharp as it warms. Cold horn, flat band.

    v ≈ 331.3 + 0.606 T m/s. 20 °C → 343.4 m/s; 30 °C → 349.5 m/s, 1.7% faster. 10 °C of warming ≈ 29 cents sharp — over a quarter of a semitone.

    Speed of sound in different conditions; v = fλ (NCERT/CBSE Class 9 ‘Sound’; NGSS HS-PS4-1).

  7. 7.Same note, different sound: seeing timbre

    ages 11–18 · 6 min
    timbregraphsdecibels
    play
    Play the same F softly, then loudly (blaring). If you have a mute, play it once more muted. A student can sing the same note.
    show
    Live lab spectrum (above)
    ask
    1. The note name didn’t change. What changed on the graph?
    2. Which harmonics grow when I play louder?
    3. Why does a loud trombone sound ‘brassy’?
    Reveal — the science

    Pitch is the spacing of the spikes — set by the lowest frequency. Timbre is the pattern of their heights. Playing loud pushes energy into the high harmonics, which is the bright brassy edge; a mute filters some harmonics out. Same spacing, different shape.

    The spikes stay at f, 2f, 3f … The vertical axis is in decibels — every 10 dB is ten times the power.

    Pitch, loudness and quality of sound (NCERT/CBSE Class 8–9 ‘Sound’); reading graphs.

  8. 8.Beats: hearing a subtraction

    ages 11–14 · 6 min
    subtractionratestuning
    play
    Two players (or the horn and a keyboard) play the same B♭, one slightly out. Slowly slide into tune.
    ask
    1. What is the wobble you can hear?
    2. Does it get faster or slower as I move into tune?
    3. How do musicians use this?
    Reveal — the science

    Two notes a few hertz apart fall in and out of step. The sound swells each time they line up: the swell happens |f₁ − f₂| times a second. When the beats stop, the two are in tune — which is exactly how brass players tune to each other.

    233 Hz against 236 Hz → 3 beats per second.

    Subtraction, rates; superposition of waves (HS physics).

Syllabus lines say which school topic each demonstration serves (CBSE/NCERT, Common Core and NGSS codes where they fit). They are pointers for the teacher, not endorsements — no exam board has reviewed Atlas.