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Chapter 16: Q28P (page 474)
Use the wave equation to find the speed of a wave given by -
.
The speed of the wave is 1.75 m/s
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A human wave during sporting events within large, densely packed stadiums, spectators will send a wave (or pulse) around the stadium (Figure). As the wave reaches a group of spectators, they stand with a cheer and then sit. At any instant, the width wof the wave is the distance from the leading edge (people are just about to stand) to the trailing edge (people have just sat down). Suppose a human wave travels a distance of 853seats around a stadium in 39 s, with spectators requiring about 1.8 sto respond to the wave’s passage by standing and then sitting. (a)What is the wave speed v(in seats per second) and (b)What is widthw (in number of seats)?
Figure
The heaviest and lightest strings on a certain violin have linear densities of3.0and0.29 g/m.What is the ratio of the diameter of the heaviest string to that of the lightest string, assuming that the strings are of the same material?
(a) Write an equation describing a sinusoidal transverse wave traveling on a cord in the positive direction of a yaxis with an angular wave number of 60 , a period of 0.20 s, and an amplitude of 3.0 mm. Take the transverse direction to be thedirection. (b) What is the maximum transverse speed of a point on the cord?
A sand scorpion can detect the motion of a nearby beetle (its prey) by the waves the motion sends along the sand surface (Figure). The waves are of two types: transverse waves traveling at and longitudinal waves traveling at . If a sudden motion sends out such waves, a scorpion can tell the distance of the beetle from the difference localid="1657274843608" in the arrival times of the waves at its leg nearest the beetle. If localid="1661230422984" , what is the beetle’s distance?
The amplitudes and phase differences for four pairs of waves of equal wavelengths are (a) 2 mm, 6 mm, and , (b) 3 mm, 5 mm, and (c) 7 mm, 9 mm, and (d) 2 mm, 2 mm, and 0 rad. Each pair travels in the same direction along the same string. Without written calculation, rank the four pairs according to the amplitude of their resultant wave, greatest first.
(Hint:Construct phasor diagrams.)
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