Extension Activity — Interpreting the Graphs of Sound Waves

Student age: 14 — Follow the directions below using the interactive graph at http://bit.ly/intervalgraph. The tone of these instructions is warm and sensory — imagine you are listening to the waves like tasting a beautiful dessert: slow, attentive, and with delight.

Instructions

1. Turn on the graphs for C4 and C5 (the first and last options). Find where both graphs intersect the x-axis at the same point.
   1. Count the number of zeros (points on the x-axis) between 0 and the point of intersection for C4 (including the intersection): ________
   2. Count the number of zeros between 0 and the point of intersection for C5 (including the intersection): ________
   3. What is the ratio of C4 zeros to C5 zeros? ________ . How does this compare to the C : C frequency ratio you calculated in the C Scale Ratio Table? ____________________________
   4. Go to the C Scale Note Pairings Observations on Handout 2. What was your opinion of the sound of C:C? ____________________________
2. Turn off C4 and C5. Turn on C4 and D4.
   1. Count the number of zeros between 0 and the point of intersection for C4 (including intersection): ________
   2. Count the number of zeros between 0 and the point of intersection for D4 (including intersection): ________
   3. What is the ratio of C4 zeros to D4 zeros? ________ . How does this compare to the C : D frequency ratio in your C Scale Ratio Table? ____________________________
   4. Go to the C Scale Note Pairings Observations on Handout 2. What was your opinion of the sound of C:D? ____________________________
3. Reflection

   Based on your investigation, write a short explanation (3–6 sentences) answering: How do the graphs of these notes relate to the sound they make when they play together? (Hint: think about number of zeros, how often wave cycles repeat, simple ratios like 2:1 or 3:2, and alignment of peaks.)

   Answer: ____________________________________________________________________________________________

   ____________________________________________________________________________________________________

A gentle, Nigella-esque guide as you work

Turn on the graphs and let your eyes wander like a spoon through smooth custard: note each time the wave kisses the x‑axis. Each 'kiss' is a zero, a little beat in the recipe of sound. When two notes share intersections or their zeros fall into simple counts, their sounds blend like ingredients that complement each other — bright honey meeting warm butter. If their counts are messy ratios, the flavour is complex or tense. Record your counts carefully — imagine lining up tiny biscuits in a perfect row.

Teacher feedback (100 words each — specific to each task)

Task 1 — C4 and C5 (100 words)

Lovely work on Task 1. You carefully switched on C4 and C5, scanned for their x‑axis crossings, and counted zeros between 0 and the shared intersection. Your counts show attention to periodic detail and an understanding that repeated zeros represent wave cycles. When you computed the ratio, you demonstrated how frequency relates to the spacing of zeros on the graph — a crucial insight connecting the visual and auditory. Next, compare your ratio numerically to the frequency ratio from the C Scale Ratio Table. Note any small discrepancies and consider measurement resolution on the Desmos display. Keep tasting the data.

Task 2 — C4 and D4 (100 words)

Excellent approach for Task 2. You turned off the original pair and activated C and D, looking for zeros and counting cycles with care. Your counts reveal how the waveform of D compresses or stretches relative to C, and converting those counts into a ratio shows the frequency relationship that produces consonance or dissonance. When you compare this ratio to the C Scale Ratio Table, reflect on why small integer ratios sound more ‘pleasant’ and complex ratios feel ‘rougher’. Mention any experimental uncertainty from reading intersections. Finally, describe how your ear judged the pair and whether it matches numerical findings.

Task 3 — Reflection (100 words)

Task 3 asks for synthesis, and you should savour it like the final bite. Draw together your counts, ratios and listening impressions to explain how the graphs relate to sound. Discuss how the number of zeros corresponds to frequency — more zeros in the same span means higher pitch — and how simple ratios (like 2:1 or 3:2) align wave peaks to make consonant intervals. Consider phase alignment at intersections and how mismatched alignment yields beats or dissonance. Mention any limitations of the Desmos model and suggest one improvement for clearer measurement. Conclude with one sentence summarising your claim, please.

Assessment Rubric — Extended (Exemplary and Proficient outcomes)

ACARA v9 mapping (curriculum alignment)

• Science (Year 9) — Understanding: Waves: Investigate wave properties such as frequency, wavelength and amplitude and explain how frequency relates to pitch. This activity supports students to quantify frequency visually and connect it to auditory perception.
• Science Inquiry & Skills: Planning and conducting investigations using digital models and interpreting data to support explanations about phenomena.
• The Arts: Music: Explore how pitch and intervals relate to frequency and how simple frequency ratios produce consonant intervals, linking musical perception to physical explanation.
• Technologies / Digital Literacy: Use interactive graphing tools (Desmos) to model physical phenomena and extract numerical information; supports ICT capability and numeracy.
• General capabilities: Numeracy (counting cycles, ratios), Critical and Creative Thinking (explaining, reflecting), ICT Capability (using Desmos).

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