Concept Focus
Emphasize that holding frequency constant while changing medium alters wavelength.
- Compare air vs. water vs. steel to show compression/expansion of λ.
- Ask: “If f doubles, what must happen to λ for v to stay fixed?”
Lab/Investigation
Use the standing wave canvas as a virtual ripple tank.
- Pause the animation and sketch nodes/antinodes.
- Assign groups to model harmonics on strings vs. pipes.
Misconception Alert
Students may think the source speed changes wave speed in the medium.
- Highlight that medium properties set v; source motion shifts perceived f.
- Discuss sonic boom limitations when vs → v.
How do I use v = f·λ?
Any two of speed (v), frequency (f), and wavelength (λ) determine the third via v = f·λ. If you choose a medium preset, v is populated automatically; otherwise, enter your own speed for custom contexts.
What speeds should I expect in common media?
Approximate wave speeds (room temperature): Air ~343 m/s (sound), Water ~1480 m/s (sound), Steel ~5960 m/s (sound). Electromagnetic waves travel at ~3×108 m/s in vacuum and slower in media by n = c/v.
How does the Doppler simulator work?
It uses the 1D acoustic Doppler shift f' = (v + vo) / (v − vs) · f with the sign convention that positive vo and vs move toward each other. If the source speed approaches v, the denominator shrinks and f' can grow very large (physically limited by shock effects, which this simple model ignores).
Why are standing waves drawn with cos(kx)·sin(ωt)?
A standing wave is the superposition of two waves with the same frequency and amplitude traveling in opposite directions. The displacement becomes y(x,t) = 2A cos(kx) sin(ωt), with nodes at kx = (n+½)π and antinodes at kx = nπ.
How does wavelength relate to harmonics on a string or air column?
For a string fixed at both ends, L contains an integer number of half-wavelengths (λn = 2L/n). For air columns, boundary conditions differ (open/closed ends), but the same v = f·λ applies to each harmonic.