KFUPM-Physics102-032
Dr.Aljalal
Sec07
Sec08
Sec09

Recitation ch 17
Answers at the end

Question 1
The equation for a transverse wave on a string is:
y(x,t) = 0.025*[sin(25*x - 500*t)]
where x and y are in meters and t is in seconds.
The tension in the string is 20 N.
Find the linear density of this string.

      a   0.05 kg/m
      b   0.13 kg/m
      c   0.02 kg/m
      d   0.25 kg/m
      e   0.50 kg/m
==============================================
Question 2
Two identical sinusoidal traveling waves are moving in
the same direction along a stretched string.
The amplitude of the resultant wave is 1.80 times that
of the common amplitude of the two combining waves.
What is the phase difference between the two waves ?

      a   90.0 degrees
      b   25.8 degrees
      c   180 degrees
      d   18.0 degrees
      e   51.7 degrees
==============================================
Question 3
A sinusoidal wave of frequency 400 Hz has a speed of
330 m/s. How far apart are two points that differ in
phase by Pi/2 ?

      a   0.137 m
      b   0.206 m
      c   1.21 m
      d   0.032 m
      e   0.825 m
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Question 4
A string has linear density = 5.1 g/m and is under a
tension of 120 N. If the vibrating length of the string
is 60 cm, What is the lowest resonant frequency?

      a   128 Hz.
      b   225 Hz.
      c   Not enough information.
      d   158 Hz.
      e   312 Hz.
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Question 5
The equation for a transverse wave on a string is:
y(x,t) = 10.0*sin(0.157*x - 50.3*t)
where x and y are in centimeters and t is in seconds.
At a given time, how far apart are two points that
differ in phase by Pi/2 radians ?

      a   0.120 cm
      b   40.0 cm
      c   10.0 cm
      d   18.0 cm
      e   5.00 cm
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Question 6
A string fixed at both ends vibrates in three loops.
The string has a length of 1.0 m, a mass of 8.0 g and
is under a tension of 15 N. What is the frequency ?

      a   150 Hz
      b   29 Hz
      c   65 Hz
      d   86 Hz
      e   130 Hz
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Question 7
A sinusoidal wave, given by the equation:

y(x,t) = 0.07 cos(6.0 x 30 t )

where x and y are in meters and t is in seconds, is
moving in a string of linear density = 1.2 g/m
At what rate is the energy transferred by the wave?

      a  1.32*10**(-2) W.
      b  2.21*10**(-2) W.
      c  3.02*10**(-2) W.
      d  1.05*10**(-2) W.
      e  No enough information is given to solve this question.
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Question 8
Sinusoidal waves are generated on a string under constant
tension by a source vibrating at a constant frequency.
If the power delivered by the vibrating source is reduced
to one half of the initial value, what is the ratio of the
final amplitude to the initial amplitude ?

      a   2.0
      b   0.50
      c   1.0
      d   0.71
      e   1.4
==============================================
Question 9
A sinusoidal wave is given by the equation:

y(x,t) = 7.0 cos(-k x w t + Phi).

Which of the following statements is true about this wave:

      a  The wave is a standing wave.
      b  The wave is moving to the positive x-axis.
      c  The wave is moving with speed kw.
      d  The wave is moving with speed k/w.
      e  The wave is moving to the negative x-axis.
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Question 10
A wave in a string, of linear density 0.13 g/m,
is given by the equation:

y(x,t) = 0.018 sin(3.0 x 24 t),

where x and y are in meters and t is in seconds.
the tension in the string is:

      a  3.90*10**(-3) N.
      b  8.32*10**(-3) N.
      c  2.43*10**(-5) N.
      d  2.34*10**(-4) N.
      e  3.12*10**(-2) N.
==============================================
Question 11
The wave function for a standing wave on a string is
y(x,t) = 2.0*sin(0.25*Pi*x)*cos(120*Pi*t)
where x and y are in centimeters and t is in seconds.
What is the distance between two adjacent nodes ?

      a   8.0 cm
      b   2.0 cm
      c   1.0 cm
      d   6.0 cm
      e   4.0 cm
==============================================
Question 12
A string having a mass per unit length of 10.0 g/m
is under a tension of 160 N. This string resonates
in the mode shown in figure 1. If the length of this
string is 90.0 cm, find the frequency of oscillation.


      a   211 Hz
      b   60.0 Hz
      c   zero
      d   120 Hz
      e   310 Hz
==============================================
Question 13
Two identical sinusoidal waves, are out of phase with each
other, travel in the same direction. They interfere and
produce a resultant wave given by the equation:

y(x,t)= 8.0*10**(-4) sin(4.0 x - 8.0 t + 1.57 rad),

where x and y are in meters and t is in seconds.
What is the amplitude of the two interfering waves?

      a   0.2 m.
      b   1.0 m.
      c   2.5 m.
      d   0.5 m.
      e   4.0 m.
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Question 14
Two sinusoidal waves having the same amplitude (A),
frequency and wavelength, travel in the same direction
and have a phase difference Phi.
Which one of the following statements is TRUE ?

      a   The resultant wave will be a standing wave for Phi = 0.
      b   For certain values of Phi, the amplitude of the
         resultant reaches 4A.
      c   Their interference will be constructive if Phi = Pi.
      d   The frequency of the resultant wave is twice the original
         frequency.
      e   Their interference will be constructive if Phi = 100 Pi.
==============================================

Answers
1     a
2     e
3     b
4     a
5     c
6     c
7     a
8     d
9     e
10     b
11     e
12     a
13     d
14     e