Chapter 17: Superposition

A steel wire is used to stretch the spring of FIGURE P17.42. An oscillating magnetic field drives the steel wire back and forth. A standing wave with three antinodes is created when the spring is stretched 8.0 cm. What stretch of the spring produces a standing wave with two antinodes?

A 75 g bungee cord has an equilibrium length of 1.20 m. The

cord is stretched to a length of 1.80 m, then vibrated at 20 Hz. This

produces a standing wave with two antinodes. What is the spring

constant of the bungee cord?

A metal wire under tension T0 vibrates at its fundamental

frequency. For what tension will the second-harmonic frequency

be the same as the fundamental frequency at tension $T_0$?

In a laboratory experiment, one end of a horizontal string is tied

to a support while the other end passes over a frictionless pulley

and is tied to a 1.5 kg sphere. Students determine the frequencies

of standing waves on the horizontal segment of the string, then

they raise a beaker of water until the hanging 1.5 kg sphere is

completely submerged. The frequency of the fifth harmonic with

the sphere submerged exactly matches the frequency of the third

harmonic before the sphere was submerged. What is the diameter

of the sphere?

A vibrating standing wave on a string radiates a sound wave with intensity proportional to the square of the standing-wave amplitude. When a piano key is struck and held down, so that the string continues to vibrate, the sound level decreases by 8.0 dB in 1.0 s. What is the string’s damping time constant t?

What is the fundamental frequency of the steel wire in FIGURE P17.48?

The two strings in FIGURE P17.49 are of equal length and are being driven at equal frequencies. The linear density of the left string is 5.0 g/m. What is the linear density of the right string?

FIGURE EX17.5 shows a standing wave oscillating at 100 Hz on a string. What is the wave speed?

If you pour liquid into a tall, narrow glass, you may hear sound with a steadily rising pitch. What is the source of the sound? And why does the pitch rise as the glass fills?

Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by fn+1 = r fn for all n. In this system, the frequency doubles every 12notes—an interval called an octave.

a. What is the value of r?

b. Orchestras tune to the note A, which has a frequency of440 Hz. What is the frequency of the next note of the scale (called A-sharp)?