 # Capitulo 21 Del Libro De Paul E. Tippens

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Chapter 21. Wave Motion

Mechanical Waves

21-1. A transverse wave has a wavelength of 30 cm and vibrates with a frequency of 420 Hz. What is the speed of this wave? [  = 30 cm = 0.30 m ]

v = f = (420 Hz)(0.30 m) ; v = 126 m/s

21-2. A person on a pier counts the slaps of a wave as the crests hit a post. If 80 slaps are heard in one minute and a particular crest travels a distance of 8 m in 4 s, what is the length of a single wave?

;  = 1.5 m

21-3. A transverse wave is pictured in Fig. 21-13. Find the amplitude, wavelength, period, and speed of the wave if it has a frequency of 12 Hz. [ A = 12 cm,  = 28 cm ]

From the figure: A = 12 cm,  = 28 cm;

v = f = (12 Hz)(0.28 m); v = 3.36 m/s

; T = 0.0833 s

21-4. For the longitudinal wave in Fig. 21-13, find the amplitude, wavelength, period, and speed of the wave if it has a frequency of 8 Hz. If the amplitude were doubled, would any of the other factors change?

From figure: A = 12 cm and  = 28 cm

v = f = (8 Hz)(0.28 m); v = 2.24 m/s; ; T = 0.125 s

21-5. A 500-g metal wire has a length of 50 cm and is under a tension of 80 N. What is the speed of a transverse wave in the wire?

; v = 8.94 m/s

21-6. If the wire in Problem 21-5 is cut in half, what will be its new mass? Show that the speed of the wave is unchanged? Why?

; m = 0.250 kg;

The speed is the same, because linear density m/l is not changed.

21-7. A 3-m cord under a tension of 200 N sustains a transverse wave speed of 172 m/s. What is the mass of the rope?

; m = 0.0203 kg

21-8. A 200-g cord is stretched over a distance of 5.2 m and placed under a tension of 500 N. Compute the speed of a transverse wave in the cord?

; v = 114 m/s

21-9. What tension is needed to produce a wave speed of 12 m/s in a 900-g string that is 2 m long?

; F = 64.8 N.

21-10. A wooden float at the end of a fishing line makes eight complete oscillations in 10 s. If it takes 3.60 s for a single wave to travel 11 m, what is the wavelength of the water waves?

;  = 3.82 m

*21-11. What frequency is required to cause a rope to vibrate with a wavelength of 20 cm when it is under a tension of 200 N. Assume the linear density of the rope to be 0.008 kg/m.

; f = 791 Hz

*21-12. A tension of 400 N causes a 300-g wire of length 1.6 m to vibrate with a frequency of 40 Hz. What is the wavelength of the transverse waves?

;  = 1.15 m

*21-13. A horizontal spring is jiggled back and forth at one end by a device that makes 80 oscillations in 12 s. What is the speed of the longitudinal waves if condensations are separated by 15 cm as the wave progresses down the spring?

v = f = (6.67 Hz)(0.15 m); v = 1.00 m/s

Energy of a Periodic Wave

21-14. A 2-m length of string has a mass of 300 g and vibrates with a frequency of 2 Hz and an amplitude of 50 mm. If the tension in the rope is 48 N, how much power must be delivered to the string?

P = 22f2A2 v = 22(2 Hz)2(0.05 m)2(0.15 kg/m)(17.9 m/s); P = 0.530 W

21-15. An 80-g string has a length of 40 m and vibrates with a frequency of 8 Hz and an amplitude of 4 cm. Find the energy per unit of length passing along the string?

; E/l = 4.04 x 10-3 J/m

21-16. If the wavelength of the transverse wave in Problem 21-11 is 1.6 m, what power is supplied by the source?

P = 5.17 x 10-2 W

*21-17. A 300-g string has a length of 2.50 m and vibrates with an amplitude of 8.00 mm. The tension in the string is 46 N. What must be the frequency of the waves in order that the average power be 90.0 W? [ P = 22f2A2 v ]

; f = 174 Hz

Standing Wave and Characteristic Frequencies

21-18. A string vibrates with a fundamental frequency of 200 Hz. What is the frequency of the second harmonic and of the third overtone?

f2 = 400 Hz

Third overtone is the fourth harmonic: f4 = 4(200 Hz); f4 = 800 Hz

21-19. If the fundamental frequency of a wave is 330 Hz, what is the frequency of the fifth harmonic and the second overtone? fn = n f1 = n(330 Hz)

f5 = 1650 Hz

Second overtone is the third harmonic: f3 = 3(330 Hz); f4 = 990 Hz

21-20. The linear density of a string is 0.00086 kg/m. What should be the tension in the rope in order for a 2 m length of this string to vibrate at 600 Hz for its third harmonic?

; F = 550 N

21-21. A 10-g string, 4 m in length, has a tension of 64 N. What is the frequency of its fundamental mode of vibration? What are the frequencies of the first and second overtones?

; f1 = 20 Hz

First Overtone = f2 = 2(20 Hz) = 40 Hz

Second Overtone = f3 = 3(20 Hz) = 60 Hz

21-22. The second harmonic of a vibrating string is 200 Hz. If the length of the string is 3 m and its tension is 200 N, compute the linear density of the string.

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