Passage VII

A student conducted experiments to determine the relationship between the musical pitch (frequency) of a vibrating string and its length, tension, and mass density (mass per unit length of string).

Experiment 1

The student cut several lengths of steel strings having different diameters. The strings were weighed and their mass densities calculated. Specified lengths of the strings were hung from the ceiling. A block was suspended from the free end of each string, making the tension in the string equal to the suspended weight in newtons (N). Plucking the string caused it to vibrate, producing sound waves. The sound waves were detected by a microphone and displayed on the screen of an oscilloscope, where the fundamental frequency of vibration, in cycles per second, or hertz (Hz), could be measured. The results are presented in Table 1.

Experiment 2

The student repeated the procedure in Experiment 1, using strings made of nylon and gut and having different diameters. The results are presented in Table 2.

40. On the Diatonic C major scale, a middle D note is taken to be 297 Hz. A guitarist wants to use a steel string of mass density 40 g/m with a tension of 3,600 N for the D string on a special type of guitar. Approximately what length of string should the guitarist use to produce a middle D note?

Answer and Explanation

Your Answer is

Correct Answer is F

Explanation

According to question 38, we know that the material does not affect the frequency, observe trail 1 and 5, and find that the shorter the rope, the higher the frequency. And when the mass density is 40 and the tension is 3600, the trail4 with a rope length of 1m can only have 150Hz, so the rope needs to be shorter. Less than 1m only has F option, 0.5m.