Figure 16-28 shows phasor diagrams for three situations in which two waves travel along the same string. All six waves have the same amplitude. Rank the situations according to the amplitude of the net wave on the string, greatest first.
The ranking of the amplitude is
The amplitude of all six waves is the same.
Determine the amplitude of the net wave using the phasor diagram
From the phasor diagrams of all three cases, we can rank them as:
Hence, the ranking of the amplitude is
Therefore, the amplitude of the net wave can be determined by the phasor diagram.
The type of rubber band used inside some baseballs and golf balls obeys Hooke’s law over a wide range of elongation of the band. A segment of this material has an un-stretched length l and a mass m. When a force F is applied, the band stretches an additional length . (a) What is the speed (in terms of m, l , and the spring constant k) of transverse waves on this stretched rubber band? (b) Using your answer to (a), show that the time required for a transverse pulse to travel the length of the rubber band is proportional to if role="math" localid="1660986246683" and is constant if .
In a demonstration, a 1.2 kg horizontal rope is fixed in place at its two ends (x = 0 and x = 2.0m) and made to oscillate up and down in the fundamental mode, at frequency 5.0 Hz. At t = 0, the point at x = 1.0m has zero displacement and is moving upward in the positive direction of a y axis with a transverse velocity of 5.0m/s. What are (a) the amplitude of the motion of that point and (b) the tension in the rope? (c) Write the standing wave equation for the fundamental mode.
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