Passage IV

When a sand-covered drumhead vibrates at certain frequencies, the sand collects at nodes (areas of least vibration). Two types of nodes can form on a vibrating drumhead: radial nodes, which look like rings, and linear nodes, which look like straight lines. As sand collects at nodes, patterns called nodal patterns (NPs) form. Figure 1 shows two NPs that can form on a sand-covered drumhead: NP 1 (a radial node only) and NP 2 (a radial node and a linear node).

Students performed 2 experiments to study the formation of NP 1 and NP 2 on various drumheads.

Experiment 1

The students obtained 5 drumheads, each having a different diameter and each set to a tension of 2,000 newtons per meter (N/m). They performed a trial with each drumhead, using the following procedure: First, they placed the drumhead directly above a speaker emitting sound waves having a frequency of 90 hertz (Hz). Then, they gradually increased the frequency until they observed NP 1. Finally, they continued to increase the frequency until they observed NP 2. Throughout each trial, the amplitude (loudness) of the sound waves was held constant. Table 1 shows the frequency at which the students observed NP 1 and NP 2 for each trial.

Experiment 2

The students performed 7 more trials with the 50 cm diameter drumhead. In each trial, first the tension was adjusted to a certain value, and then the procedures of the Experiment 1 trials were repeated. Figure 2 shows the results for each trial, as well as a line of best fit for each NP.