Passage VI

A standing wave on a taut string is a wave that appears to vibrate without traveling along the string. Such waves are called the string's harmonics. Each harmonics has a characteristic number of nodes: locations between the ends of the string that do not move (the ends of the string do not count as nodes). Figure 1 illustrates a harmonic and also the apparatus that a student used to be perform 2 experiments on standing waves.

A string having an a mass per unit length of µ was attached on one end an oscillator (a motor that vibrates) and on the other end to a pulley and ratchet. The student could select the frequency, f (the number of cycles per second), of the oscillator's vibration. By cranking the ratchet, the student could vary the force of tension, T , in the string.

Experiment 1

With 0.10 newtons (N) of tension in String X (µ = 0.02 g/cm), the student varied f. She noted that standing waves occurred only at certain values of f. The student sketched the first 5 harmonics and recorded f (in hertz, Hz) for each. She repeated this procedure for Sting Y (μ = 0.08 g/cm ) and for String Z (μ = 0.16 g/cm). See table 1.

Experiment 2

Beginning again with String X, the student set the oscillator to vibrate at f = 25.0 Hz. She then varied T, and noted that standing waves occurred only at certain values of T. The student recorded T for the first 5 harmonics. She repeated this procedure for String Y and Z. See Table 2.