Apply a wave-speed model

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: Wave speed equals frequency in hertz multiplied by wavelength in meters. Formula: a*b. Variable key: a = frequency (Hz), b = wavelength (m)
• Distinct worked inputs and result: A distinct generic wave is 3 Hz with wavelength 2 m: 3×2=6 m/s.
• Assessment case 1: Supplied case 1: frequency (Hz)=4; wavelength (m)=2, using the explicitly named quantities. Wave speed equals frequency in hertz multiplied by wavelength in meters. What result follows?
• Assessment case 2: Supplied case 2: frequency (Hz)=5; wavelength (m)=3, using the explicitly named quantities. Wave speed equals frequency in hertz multiplied by wavelength in meters. What result follows?
• Assessment case 3: Supplied case 3: frequency (Hz)=6; wavelength (m)=1.5, using the explicitly named quantities. Wave speed equals frequency in hertz multiplied by wavelength in meters. What result follows?
• Assessment case 4: Supplied case 4: frequency (Hz)=8; wavelength (m)=2, using the explicitly named quantities. Wave speed equals frequency in hertz multiplied by wavelength in meters. What result follows?
• Assessment case 5: Supplied case 5: frequency (Hz)=10; wavelength (m)=0.5, using the explicitly named quantities. Wave speed equals frequency in hertz multiplied by wavelength in meters. What result follows?
• Assessment case 6: Supplied case 6: frequency (Hz)=12; wavelength (m)=0.25, using the explicitly named quantities. Wave speed equals frequency in hertz multiplied by wavelength in meters. What result follows?

Learn the idea

Wave speed equals frequency times wavelength. Use meters and hertz for meters per second. These small supplied values describe a generic wave model, not actual light speed.

Wave speed equals frequency in hertz multiplied by wavelength in meters. The formula in the supplied model is a*b. Variable key: a = frequency (Hz), b = wavelength (m). Use wavelength in meters. Generic model values are not actual electromagnetic vacuum speed.

A distinct generic wave is 3 Hz with wavelength 2 m: 3×2=6 m/s. Frequency times wavelength gives speed. 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 frequency (Hz)=5; wavelength (m)=2. Expected result: 10 m/s. Explain what changes and keep this assumption: Frequency times wavelength gives speed.

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