Measure a repeated wavelength

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Wavelength equals span divided by complete wavelengths. Formula: a/b. Variable key: a = total span (cm), b = complete wavelengths
• Distinct worked inputs and result: A distinct model spans 14 cm across 2 full wavelengths: 14/2=7 cm.
• Assessment case 1: Supplied case 1: total span (cm)=12; complete wavelengths=3, using the explicitly named quantities. Wavelength equals span divided by complete wavelengths. What result follows?
• Assessment case 2: Supplied case 2: total span (cm)=20; complete wavelengths=4, using the explicitly named quantities. Wavelength equals span divided by complete wavelengths. What result follows?
• Assessment case 3: Supplied case 3: total span (cm)=18; complete wavelengths=3, using the explicitly named quantities. Wavelength equals span divided by complete wavelengths. What result follows?
• Assessment case 4: Supplied case 4: total span (cm)=16; complete wavelengths=4, using the explicitly named quantities. Wavelength equals span divided by complete wavelengths. What result follows?
• Assessment case 5: Supplied case 5: total span (cm)=30; complete wavelengths=5, using the explicitly named quantities. Wavelength equals span divided by complete wavelengths. What result follows?
• Assessment case 6: Supplied case 6: total span (cm)=24; complete wavelengths=6, using the explicitly named quantities. Wavelength equals span divided by complete wavelengths. What result follows?

Learn the idea

Use matching points and consistent distance units. A crest-to-trough distance is not one full wavelength in the regular model. Divide the total length by complete repetitions.

Wavelength equals span divided by complete wavelengths. The formula in the supplied model is a/b. Variable key: a = total span (cm), b = complete wavelengths. Count full matching-point intervals. State the centimeter unit.

A distinct model spans 14 cm across 2 full wavelengths: 14/2=7 cm. The model assumes equally spaced repeats. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with total span (cm)=13; complete wavelengths=3. Expected result: approximately 4.3333333 cm. Explain what changes and keep this assumption: The model assumes equally spaced repeats.

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