Trumpet
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♭ or C trumpet 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 valve combination. The class’s own numbers make the graph — predictions, error and all.

live lab · play the real trumpet

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. (open)

—

pick the tube below

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

the tube you’re playing

Open: lowest possible note (the pedal) ≈ 116.5 Hz. Every note you can play here is a whole-number multiple of it.

Try: the G on the staff open, then 2, 1, 1+2, 2+3, 1+3, 1+2+3 without touching the slides — capture each and watch 1+3 and 1+2+3 drift sharp.

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

the run-sheet

8 demonstrations with the real trumpet

  1. 1.Lips as a valve

    ages 11–14 · 6 min
    vibrationfrequencyresonance
    play
    Buzz a siren on the mouthpiece alone (it can slide anywhere). Then put it in the trumpet and try to slide — it jumps from note to note.
    show
    Live lab — big numbers (above)
    ask
    1. On the mouthpiece the pitch slid smoothly. Why does the trumpet only allow certain notes?
    2. What sets those notes — the lips or the tube?
    Reveal — the science

    The lips can buzz at any speed, but the air column only resonates at certain frequencies and it pulls the lips onto them. That is why the pitch 'clicks' between notes on the horn.

    Middle-of-the-staff written G on a B♭ trumpet sounds concert F, about 349 Hz: 349 lip vibrations per second.

    Sound as vibration; resonance (NGSS MS-PS4-1).

  2. 2.A bugle call with no valves

    ages 11–18 · 8 min
    ratioharmonic serieschords
    play
    No valves at all: play ‘Taps’ or any bugle call. It only uses written G, C, E and the high G.
    ask
    1. How can you play a tune without pressing anything?
    2. Why do bugle calls all sound like the same chord?
    3. Measure two of the notes. What is the ratio?
    Reveal — the science

    Those four notes are harmonics 3, 4, 5 and 6 of the open tube. Their frequencies are in the ratio 3 : 4 : 5 : 6, and those ratios are a major chord — which is why every bugle call is built from one chord.

    G→C = 4 : 3 (a fourth), C→E = 5 : 4 (a major third), E→G = 6 : 5 (a minor third).

    Ratio (CCSS 6.RP.A.1); harmonics in pipes (HS physics).

  3. 3.Three switches, eight combinations, seven notes

    ages 11–14 · 8 min
    combinatoricspowers of 2subset sums
    play
    Hold written G and press: none, 2, 1, 1+2, 2+3, 1+3, 1+2+3 — a chromatic scale down. Then show that 3 alone gives the same note as 1+2.
    ask
    1. Three valves, each up or down. How many combinations?
    2. So why only seven different notes?
    3. Valve 2 lowers 1 semitone, valve 1 lowers 2, valve 3 lowers 3. Which totals can you make?
    Reveal — the science

    Each valve is a yes/no switch, so there are 2 × 2 × 2 = 8 combinations. The amounts they lower are 1, 2 and 3 semitones; the subsets add up to 0, 1, 2, 3, 3, 4, 5, 6 — the total 3 appears twice (1+2 and 3 alone), so eight combinations give seven notes.

    2³ = 8. Subset sums of {1, 2, 3}: 0, 1, 2, 3, 3, 4, 5, 6.

    Counting principle and powers; binary (CCSS 7.SP.C.8 compound events; computing).

  4. 4.Why 1 + 3 is out of tune — measured

    ages 14–18 · 12 min
    exponentspercentageserror
    play
    Do not touch any valve slide. On the written G harmonic play: open, 2, 1, 1+2, 2+3, 1+3, 1+2+3 (G, F♯, F, E, E♭, D, C♯). Capture each in the data logger.
    ask
    1. Which notes land above the prediction line?
    2. Valve 1 adds 12% to the tube and valve 3 adds 19%. Together?
    3. But how much longer does the tube need to be for five semitones?
    Reveal — the science

    Each valve is built to be right on its own. But lowering five semitones needs the whole tube × 1.335 (33.5% more), and valves 1 and 3 together add only 12.2% + 18.9% = 31.2%. Lengths add; pitches multiply. The note comes out sharp — which is why trumpets have finger rings to pull the 1st and 3rd valve slides out.

    2^(2/12) − 1 = 0.122; 2^(3/12) − 1 = 0.189; sum 0.312 < 2^(5/12) − 1 = 0.335 ⇒ ≈ 30 cents sharp on a horn with exactly-tuned valves (real horns are built with a long 3rd slide, so you may measure less).

    Laws of indices: why 2^a + 2^b ≠ 2^(a+b) (CCSS HSN-RN.A.1); percentage change.

  5. 5.Trumpet and trombone: twice the tube, an octave down

    ages 12–18 · 8 min
    ratiomodellingmeasurement
    play
    Each instrument plays its lowest ordinary open note — trumpet: written middle C, no valves; trombone: B♭ on the second line of the bass staff, 1st position. Both are harmonic 2 of their tubes. Then measure both instruments’ tubing with string.
    show
    Live lab — compare the two frequencies (above)
    ask
    1. Both are ‘in B♭’ and both played harmonic 2. What is the frequency ratio between them?
    2. The string says about 1.5 m and 2.7 m. Is that exactly 2 : 1?
    3. Why might the length the sound ‘feels’ differ from the tape-measure length?
    Reveal — the science

    The trombone sounds exactly an octave below the trumpet, so its air column acts exactly twice as long. Measured with string the tubes are close to 2 : 1 but not exact: the mouthpiece and the flaring bell change where the sound wave really reflects. A good lesson in a model (a simple tube) versus the real object.

    Trumpet ≈ 233 Hz, trombone ≈ 117 Hz: ratio 2 : 1, an octave. B♭ trumpet ≈ 1.48 m of tube; tenor trombone ≈ 2.7–2.8 m.

    Ratio and proportion; mathematical modelling and its limits.

  6. 6.Does coiling the tube change the note?

    ages 11–14 · 5 min
    measurementmodels
    play
    Play a note; then hold up a straight garden-hose ‘trumpet’ (hose + funnel + mouthpiece, about 1.5 m) and play the same bugle notes.
    ask
    1. The trumpet is wrapped up; the hose is straight. Same notes?
    2. So why do makers coil it?
    Reveal — the science

    The sound wave follows the tube; gentle bends barely matter, so a coiled 1.48 m tube and a straight 1.48 m hose give the same harmonic series. Coiling just makes it something you can hold.

    Length, not shape, sets the harmonic series: f₁ ≈ v ÷ (2L).

    Measurement; testing a prediction.

  7. 7.Seeing timbre (and what a mute does)

    ages 11–18 · 6 min
    timbregraphsfilters
    play
    Same written G: soft, loud, then with a straight or cup mute if you have one.
    show
    Live lab spectrum (above)
    ask
    1. What stayed the same on the graph? What changed?
    2. Which spikes does the mute cut?
    Reveal — the science

    Pitch is the spacing of the spikes; timbre is their heights. Loud playing feeds the high harmonics (the bright edge); a mute removes some and the colour changes while the note stays the same.

    Spikes at f, 2f, 3f …; vertical axis in decibels.

    Pitch, loudness, quality (NCERT/CBSE Class 8–9 ‘Sound’).

  8. 8.Warm air, sharp horn

    ages 13–18 · 5 min
    speed of soundtemperature
    play
    Long written C on a cold horn; breathe warm air through for 20 seconds; play again.
    show
    Live lab — try the temperature box (above)
    ask
    1. Why does the pitch rise as the horn warms?
    2. Which part of v = fλ changed?
    Reveal — the science

    Warm air carries sound faster; the tube fixes the wavelength, so the frequency rises — the horn goes sharp as it warms.

    v ≈ 331.3 + 0.606 T. 10 °C warmer ≈ 1.7% faster ≈ 29 cents sharp.

    v = fλ (NGSS HS-PS4-1; NCERT/CBSE Class 9 ‘Sound’).

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.