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Unformatted text preview: of oscillation for the pendulum is
T, determine the speed of a transverse wave in the
string when the pendulum hangs at rest.
17. The elastic limit of a piece of steel wire is 2.70 109 Pa.
What is the maximum speed at which transverse wave
pulses can propagate along this wire before this stress is
exceeded? (The density of steel is 7.86 103 kg/m3.)
18. Review Problem. A light string with a mass per unit
length of 8.00 g/m has its ends tied to two walls separated by a distance equal to threefourths the length of
the string (Fig. P16.18). An object of mass m is sus3L/4 L/2 L/2 2 and m y2 5
(3x 4t 6)2 2 Figure P16.18 514 CHAPTER 16 Wave Motion
the period of vibration from this plot and compare your
result with the value found in Example 16.3.
24. For a certain transverse wave, the distance between two
successive crests is 1.20 m, and eight crests pass a given
point along the direction of travel every 12.0 s. Calculate the wave speed.
25. A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in
30.0 s. Also, a given maximum travels 425 cm along the
rope in 10.0 s. What is the wavelength?
26. Consider the sinusoidal wave of Example 16.3, with the
wave function pended from the center of the string, putting a tension
in the string. (a) Find an expression for the transverse
wave speed in the string as a function of the hanging
mass. (b) How much mass should be suspended from
the string to produce a wave speed of 60.0 m/s?
19. Review Problem. A light string with a mass of 10.0 g
and a length L 3.00 m has its ends tied to two walls
that are separated by the distance D 2.00 m. Two objects, each with a mass M 2.00 kg, are suspended
from the string, as shown in Figure P16.19. If a wave
pulse is sent from point A , how long does it take for it
to travel to point B ?
20. Review Problem. A light string of mass m and length L
has its ends tied to two walls that are separated by the
distance D. Two objects, each of mass M, are suspended
from the string, as shown in Figure P16.19. If a wave
pulse is sent from point A, how long does it take to
travel to point B ? L
4
A B
L
2 M M Figure P16.19 WEB y Problems 19 and 20. y Section 16.6 Reﬂection and Transmission Section 16.7 Sinusoidal Waves
23. (a) Plot y versus t at x 0 for a sinusoidal wave of the
form y (15.0 cm) cos(0.157x 50.3t ) , where x and y
are in centimeters and t is in seconds. (b) Determine (0.25 m) sin(0.30x 40t ) where x and y are in meters and t is in seconds. Determine for this wave the (a) amplitude, (b) angular frequency, (c) angular wave number, (d) wavelength,
(e) wave speed, and (f) direction of motion.
30. A transverse wave on a string is described by the expression 21. A 30.0m steel wire and a 20.0m copper wire, both with
1.00mm diameters, are connected end to end and are
stretched to a tension of 150 N. How long does it take a
transverse wave to travel the entire length of the two
wires? 22. A series of pulses, each of amplitude 0.150 m, are sent
down a string that is attached to a post at one end. The
pulses are reﬂected at the post and travel back along
the string without loss of amplitude. What is the displacement at a point on the string where two pulses are
crossing (a) if the string is rigidly attached to the post?
(b) if the end at which reﬂection occurs is free to slide
up and down? 50.3t ) At a certain instant, let point A be at the origin and
point B be the ﬁrst point along the x axis where the
wave is 60.0° out of phase with point A. What is the
coordinate of point B ?
27. When a particular wire is vibrating with a frequency of
4.00 Hz, a transverse wave of wavelength 60.0 cm is produced. Determine the speed of wave pulses along the
wire.
28. A sinusoidal wave traveling in the x direction (to the
left) has an amplitude of 20.0 cm, a wavelength of
35.0 cm, and a frequency of 12.0 Hz. The displacement
of the wave at t 0, x 0 is y
3.00 cm; at this same
point, a particle of the medium has a positive velocity.
(a) Sketch the wave at t 0. (b) Find the angular wave
number, period, angular frequency, and wave speed of
the wave. (c) Write an expression for the wave function
y (x, t ).
29. A sinusoidal wave train is described by the equation D
L
4 (15.0 cm) cos(0.157x y WEB (0.120 m) sin( x/8 4 t) (a) Determine the transverse speed and acceleration of
the string at t 0.200 s for the point on the string located at x 1.60 m. (b) What are the wavelength, period, and speed of propagation of this wave?
31. (a) Write the expression for y as a function of x and t
for a sinusoidal wave traveling along a rope in the
negative x direction with the following characteristics:
A 8.00 cm,
80.0 cm, f 3.00 Hz, and y(0, t ) 0
at t 0. (b) Write the expression for y as a function of
x and t for the wave in part (a), assuming that
y(x, 0) 0 at the point x 10.0 cm.
32. A transverse sinusoidal wave on a string has a period
T 25.0 ms and travels in the negative x direction with
a speed of 30.0 m/s. At t 0, a particle on the string...
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This note was uploaded on 03/24/2010 for the course PHYSICS 2202 taught by Professor Mihalisin during the Spring '09 term at Temple.
 Spring '09
 MIHALISIN
 Physics

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