This simulation shows the standing waves that occur when waves reflecting from each end of a string or air column interfere constructively. This is what happens in musical instruments, for example, although a musical note is generally composed of a fundamental (lowest frequency standing wave) and several harmonics, unlike the single-frequency situation shown here. This string is driven from the left end at the chosen frequency, and the standing wave pattern builds up gradually as reflections occur at the two ends. Here are some things to investigate:

1. | With the string fixed at both ends, the fundamental frequency is 2 Hz. What is the relationship between L, the length of the string, and l, the wavelength?

2. | With the string fixed at both ends, what happens when the frequency is 1 Hz? Why?

3. | With the string fixed at both ends, see if you can determine a relationship between the length of the string and the wavelengths of the waves that produce standing waves.

4. | Repeat with the string free at both ends. Is the relationship the same, or different? Why?

5. | Repeat with the string free at one end only. What is the frequency of the fundamental now? What is the relationship between the length of the string and the wavelengths of the standing waves?