C.2 · 波动模型

What would explain this observation?

• A wave can carry energy across water while a floating marker mainly oscillates. Energy transfer and bulk transfer of matter are different.
• Start with a prediction. State the quantities or features you would compare, then decide what evidence could distinguish two explanations.

Build the model

• Frequency 频率 is oscillations per time; wavelength 波长 is distance between successive points in phase. Wave speed equals frequency multiplied by wavelength. Transverse oscillations are perpendicular to propagation.
• wavelength: Distance between successive points in phase; frequency: Number of oscillations per unit time.

Choose evidence that can test it

• At a boundary, frequency stays fixed by the source. A change of speed changes wavelength. Refraction follows from speed differences; angles are measured from the normal.
• Measure several wavelengths and divide to reduce fractional reading uncertainty. Use a ray box with a normal drawn at the boundary. Keep the beam away from eyes and record incident and refracted angles clearly.

Work from known quantities

• State the known values and their units. Choose the relation because its assumptions fit this case, then rearrange before substitution.
• Known: frequency 5 Hz and wavelength 0.40 m. Use v = fλ. v = 5×0.40 = 2.0 metres per second. If speed falls to 1.5 metres per second at the same frequency, wavelength = v/f = 1.5/5 = 0.30 m.

Example:

Frequency is 8 Hz and wavelength is 0.25 m. Find wave speed. Use the same sequence: known quantities → model → relation → substitution → unit and interpretation.

Check the conclusion and its limits

• The wave frequency does not change simply because the medium changes. A longitudinal wave has oscillations parallel to propagation.
• Return to the original observation. Explain what the result supports, which conditions it assumes, and one way to test a competing explanation.

Warn:

Wave frequency always changes when a wave enters a new medium. This claim is false: The wave frequency does not change simply because the medium changes. A longitudinal wave has oscillations parallel to propagation.

Key:

Waves, measurement and refraction: At a boundary, frequency stays fixed by the source. A change of speed changes wavelength. Refraction follows from speed differences; angles are measured from the normal.