Chapter 11: 11-52P (page 292)
The speed of waves on a string is \({\bf{97}}{\rm{ }}{\bf{m}}{\rm{/}}{\bf{s}}\).If the frequency of standing waves is 475 Hz, how far apart are two adjacent nodes?
The length between two adjacent nodes is \(0.10{\rm{ m}}\).
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Carbon dioxide is a linear molecule. The carbon–oxygen bonds in this molecule act very much like springs. Figure 11–58 shows one possible way the oxygen atoms in this molecule can oscillate: the oxygen atoms oscillate symmetrically in and out, while the central carbon atom remains at rest. Hence each oxygen atom acts like a simple harmonic oscillator with a mass equal to the mass of an oxygen atom. It is observed that this oscillation occurs at a frequency \(f{\bf{ = 2}}{\bf{.83 \times 1}}{{\bf{0}}^{{\bf{13}}}}\;{\bf{Hz}}\). What is the spring constant of the C-O bond?
Consider a wave traveling down a cord and the transverse motion of a small piece of the cord. Which of the following is true?
(a) The speed of the wave must be the same as the speed of a small piece of the cord.
(b) The frequency of the wave must be the same as the frequency of a small piece of the cord.
(c) The amplitude of the wave must be the same as the amplitude of a small piece of the cord.
(d) All of the above are true.
(e) Both (b) and (c) are true.
What, approximately, is the percent uncertainty for a measurement given as\({\bf{1}}{\bf{.57 }}{{\bf{m}}^{\bf{2}}}\)?
One end of a horizontal string is attached to a small amplitude mechanical 60.0-Hz oscillator. The string’s mass per unit length is\({\bf{3}}.{\bf{5}} \times {\bf{1}}{{\bf{0}}^{ - {\bf{4}}}}{\rm{ }}{\bf{kg}}{\rm{/}}{\bf{m}}\). The string passes over a pulley, a distance \({\bf{l}} = {\bf{1}}.{\bf{50}}{\rm{ }}{\bf{m}}\)away, and weights are hung from this end, Fig. 11–55. What mass m must be hung from this end of the string to produce (a) one loop, (b) two loops, and (c) five loops of a standing wave? Assume the string at the oscillator is a node, which is nearly true.
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