Physics · Waves · Sound / Principles and Exploration
Resonance and standing waves — principles and investigation
If you fix both ends of the string and shake it, a large amplitude and consistent pattern will appear at a certain frequency. Observe resonance and standing waves by changing the string length, wave speed, driving frequency, and attenuation. This is an activity that connects the position of the node with the smallest movement and the position of the ship that shakes the most with the wavelength.
How does it work?
The fixed string at both ends contains n half-wavelengths. The response is maximum at resonance in the selected mode.
fₙ = n·v / (2L)
Try this investigation
- Find the node and belly of the selected mode. Change the driving frequency and compare the amplitude.
- L=1 m, v=10 m/s, record 4, 5, 6 Hz in mode 1.
- Change the mode, attenuation, and length one by one and record.
Interpreting your results
What is the driving frequency with the largest amplitude in mode 1?
The selected mode resonance curve is maximum at f₁=5 Hz.
Assumptions and limitations
It is a steady-state envelope approximation that is fixed at both ends and represents only one selected mode of a linear string. Synthesis of multiple modes, transient response, and driving position effects are omitted. Use the response A=(0.015/attenuation)/√[1+((f−fₙ)/(attenuation·fₙ))²] m. For resonances outside the operable driving range, the Fit button stays at the range boundary. The sound is 100 times the driving frequency.