20. Energy in waves. As a sine-shaped wave moves along a stretched string, each coil os...
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20. Energy in waves. As a sine-shaped wavemoves along a stretched string, each coil os the spring willexecute the simple harmonic motion. Suppose that a spring withlinear density µ= 0.40 kg/m has a tension T=1.6N in it and that asine-shaped wave of amplitude 10cm and wavelength of 1.5 is movingalong the sprig. Consider a 1cm segment of the spring.
a. What is the mass of the 1cm segment of the spring?
b. What is the speed of the wave along the spring?
c. What is the period of the simple harmonic motion executed bythis segment of the spring?
d. Knowing the mass of the segment and the period of its simpleharmonic motion, find the effective spring constant of the coilspring for transverse displacements away from its equilibrium.
e. What is the total energy of the simple harmonic oscillator ofthe segment?
f. There are 150 1cm segments within the 1.5-meter wavelength.What will be the total harmonic oscillation energy in onewavelength of the wave?
g. At what rate in joules/seconds (or with what power in watts)will this energy be transferred past a given point on thespring?
20. Energy in waves. As a sine-shaped wavemoves along a stretched string, each coil os the spring willexecute the simple harmonic motion. Suppose that a spring withlinear density µ= 0.40 kg/m has a tension T=1.6N in it and that asine-shaped wave of amplitude 10cm and wavelength of 1.5 is movingalong the sprig. Consider a 1cm segment of the spring.
a. What is the mass of the 1cm segment of the spring?
b. What is the speed of the wave along the spring?
c. What is the period of the simple harmonic motion executed bythis segment of the spring?
d. Knowing the mass of the segment and the period of its simpleharmonic motion, find the effective spring constant of the coilspring for transverse displacements away from its equilibrium.
e. What is the total energy of the simple harmonic oscillator ofthe segment?
f. There are 150 1cm segments within the 1.5-meter wavelength.What will be the total harmonic oscillation energy in onewavelength of the wave?
g. At what rate in joules/seconds (or with what power in watts)will this energy be transferred past a given point on thespring?
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