Relate frequency and 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 in meters equals wave speed in meters per second divided by frequency in hertz. Formula: a/b. Variable key: a = wave speed (m/s), b = frequency (Hz)
• Distinct worked inputs and result: A distinct generic wave travels 18 m/s at 3 Hz: wavelength 18/3=6 m.
• Assessment case 1: Supplied case 1: wave speed (m/s)=24; frequency (Hz)=6, using the explicitly named quantities. Wavelength in meters equals wave speed in meters per second divided by frequency in hertz. What result follows?
• Assessment case 2: Supplied case 2: wave speed (m/s)=30; frequency (Hz)=5, using the explicitly named quantities. Wavelength in meters equals wave speed in meters per second divided by frequency in hertz. What result follows?
• Assessment case 3: Supplied case 3: wave speed (m/s)=40; frequency (Hz)=8, using the explicitly named quantities. Wavelength in meters equals wave speed in meters per second divided by frequency in hertz. What result follows?
• Assessment case 4: Supplied case 4: wave speed (m/s)=36; frequency (Hz)=9, using the explicitly named quantities. Wavelength in meters equals wave speed in meters per second divided by frequency in hertz. What result follows?
• Assessment case 5: Supplied case 5: wave speed (m/s)=48; frequency (Hz)=12, using the explicitly named quantities. Wavelength in meters equals wave speed in meters per second divided by frequency in hertz. What result follows?
• Assessment case 6: Supplied case 6: wave speed (m/s)=60; frequency (Hz)=10, using the explicitly named quantities. Wavelength in meters equals wave speed in meters per second divided by frequency in hertz. What result follows?

Learn the idea

For a fixed wave speed, wavelength is speed divided by frequency. Increasing frequency shortens wavelength under that fixed-speed assumption. These values describe a generic wave, not vacuum light.

Wavelength in meters equals wave speed in meters per second divided by frequency in hertz. The formula in the supplied model is a/b. Variable key: a = wave speed (m/s), b = frequency (Hz). Use a fixed specified propagation speed. Frequency is not the wave’s spatial separation.

A distinct generic wave travels 18 m/s at 3 Hz: wavelength 18/3=6 m. These generic model speeds are not light 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 wave speed (m/s)=25; frequency (Hz)=6. Expected result: approximately 4.1666667 m. Explain what changes and keep this assumption: These generic model speeds are not light speed.

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