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Chapter 16: Q47P (page 474)
One of the harmonic frequencies for a particular string under tension is 325 Hz.The next higher harmonic frequency is 390 Hz. What harmonic frequency is next higher after the harmonic frequency 195 Hz?
The harmonic frequency that is next higher after the harmonic frequency 195 Hz is 260 Hz.
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Body armor. When a high-speed projectile such as a bullet or bomb fragment strikes modern body armor, the fabric of the armor stops the projectile and prevents penetration by quickly spreading the projectile’s energy over a large area. This spreading is done by longitudinal and transverse pulses that move radiallyfrom the impact point, where the projectile pushes a cone-shaped dent into the fabric. The longitudinal pulse, racing along the fibers of the fabric at speedahead of the denting, causes the fibers to thin and stretch, with material flowing radially inward into the dent. One such radial fiber is shown in Fig. 16-48a. Part of the projectile’s energy goes into this motion and stretching. The transverse pulse, moving at a slower speed, is due to the denting. As the projectile increases the dent’s depth, the dent increases in radius, causing the material in the fibers to move in the same direction as the projectile (perpendicular to the transverse pulse’s direction of travel). The rest of the projectile’s energy goes into this motion. All the energy that does not eventually go into permanently deforming the fibers ends up as thermal energy. Figure 16-48bis a graph of speed vversus time tfor a bullet of mass 10.2g fired from a .38 Special revolver directly into body armor. The scales of the vertical and horizontal axes are set byand. Take, and assume that the half-angle of the conical dent is. At the end of the collision, what are the radii of (a) the thinned region and (b) the dent (assuming that the person wearing the armor remains stationary)?
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 land a mass m. When a force Fis 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 .
The equation of a transverse wave traveling along a string is in which xand yis in meters and tis in seconds. (a) What is the displacement yat x=2.3 m,t=0.16 s? A second wave is to be added to the first wave to produce standing waves on the string. If the second wave is of the form, what are (b), (c)k, (d), and (e) the correct choice of sign in front ofvfor this second wave? (f) What is the displacement of the resultant standing wave at x =2.3 m,t =0.16 s?
A generator at one end of a very long string creates a wave given by
and a generator at the other end creates the wave
Calculate the (a) frequency, (b) wavelength, and (c) speed of each wave.
For , what is the location of the node having the (d) smallest, (e) second smallest, and (f) third smallest value of x? For, what is the location of the antinode having the (g) smallest, (h) second smallest, and (i) third smallest value of?
Two sinusoidal waves of the same period, with amplitudes of 5.0and 7.0 mm, travel in the same direction along a stretched string; they produce a resultant wave with an amplitude of 9.0 mm. The phase constant of the 5.0 mmwave is 0.What is the phase constant of the 7.0 mmwave?
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