Sinai University
Faculty of Engineering Sciences
Department of Basic Sciences
Student name:
ID:___
______ Group:
Physics1: BSM 022
Time: ½ hour
Date: 11/4/2012
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1- A sinusoidal transverse wave is traveling on a string. Any point on the string:
A. moves in the same direction as the wave
B. moves in simple harmonic motion with a different frequency than that of the wave
C. moves in simple harmonic motion with the same angular frequency as the wave
D. moves in uniform circular motion with a different angular speed than the wave
E. moves in uniform circular motion with the same angular speed as the wave
1-2 Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:
A. the magnitude of its acceleration is a maximum
B. the magnitude of its displacement is a maximum
C. the magnitude of its displacement is a minimum
D. the magnitude of its displacement is half the amplitude
E. the magnitude of its displacement is one-fourth the
1-3 An electron volt is :
1-3 The speed of a sinusoidal wave on a string depends on:
A. the frequency of the wave
B. the wavelength of the wave
C. the length of the string
D. the tension in the string
E. the amplitude of the wave
1-4 For a given medium, the frequency of a wave is:
A. independent of wavelength
B. proportional to wavelength
C. inversely proportional to wavelength
D. proportional to the amplitude
E. inversely proportional to the amplitude
1-5If y = 0.02 sin (30x – 400t) (SI units), the frequency of the wave is
a. 30 Hz
b. 15/π Hz
c. 200/π Hz
d. 400 Hz
e. 800π Hz
1-6 Two ropes are spliced together as shown.
A short time after the incident pulse shown in the diagram reaches the splice, the ropes appearance will be that
in
(a)
(b)
(c)
(d)
(e)
-Problems :
1-A wave is described by y = (2.00 cm)sin (kx - t), where k = 2.11 rad/m, = 3.62 rad/s, x and y are in
meters, and t is in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, and (d) the
speed of the wave
2-
Prove
The rate of energy transfer by sinusoidal wave on string:
Consider a sinusoidal wave traveling on a string, Let’s focus our attention on an infinitesimal element of the string
of length dx and mass dm, All elements have the same angular frequency v and the same amplitude A. The kinetic
energy K associated with a moving particle is K = 1/2mv2 If we apply this equation to the infinitesimal element, the
kinetic energy dK associated with the up and down motion of this element is
where vy is the transverse speed of the element. If  is the mass per unit length of the string, the mass dm of the
element of length dx is equal to  dx. Hence, we can express the kinetic energy of an element of the string as
Substituting for the general transverse speed of an element of the medium:
If we take a snapshot of the wave at time t 5 0, the kinetic energy of a given element is
In addition to kinetic energy, there is potential energy associated with each element of the string due to its
displacement from the equilibrium position and the restoring forces from neighboring elements. A similar analysis
to that above for the total potential energy U in one wavelength gives exactly the same result:
The total energy in one wavelength of the wave is the sum of the potential and kinetic energies:
Rate of energy transfer:
2- The Speed of Waves on Strings:
The small element of the string of length s forms an approximate arc of a circle of radius R. In the moving frame
ofreference (which moves to the right at a speed v along with the pulse), the shaded element moves to the left
with a speed v. This element has a centripetal acceleration equal to v2/R, which is supplied by components of the
force TS whose magnitude is the tension in the string. The force TS acts on both sides of the element and is tangent
to the arc as shown in Figure . The horizontal components of TScancel, and each vertical component T sin u acts
downward. Hence, the total force on the element is 2T sin u toward the arc’s center. Because the element is small,
u is small, and we can therefore use the small-angle approximation sin u < u. So, the total radial force is