Physics 2130
Midterm Examination
Spring 2006
ID #:
Name:
Hand in the question sheet with the exam booklet.
For questions 1 to 6 circle the correct answer.
1- The ideal mechanical advantage (i.e. the ratio of the weight W to the pull P for equilibrium) of
the combination of pulleys shown is:
a) 1
b) 2
c) 1.5 d) 4
e) 5
2- A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 × 109
N/m2. When it is subjected to a pressure of 3.0 × 105 Pa its volume is:
a) 7.31 cm3
b) 7.99931 cm3
c) 8.00069 cm3
d) 8.69 cm3
e) none of these
3- A bucket resting on the floor of an elevator contains an incompressible fluid of density ρ. When
the elevator has a downward acceleration a, the pressure difference between two points in the fluid
separated by a vertical distance Δh is given by:
a) ρaΔh
b) ρgΔh
c) ρ(g + a)Δh
d) ρ(g – a)Δh
4- A solid has a volume of 8 cm3. When weighed on a spring scale calibrated in grams, the scale
indicates 20 g. What does the scale indicate if the object is weighed while immersed in a liquid of
density 2 g/cm3?
a)4 g
b) 10g
c) 16 g
d) 0 g
Physics 2130
Midterm Examination
Spring 2006
ID #:
Name:
5- During a time interval of exactly one period of vibration of a tuning fork, the emitted sound
travels a distance:
a) equal to the length of the tuning fork
b) equal to twice the length of the tuning fork
c) of about 330 m
d) which decreases with time
e) of one wavelength in air
6- The mathematical forms for three sinusoidal traveling waves are gives by
wave 1: y(x, t) = (2 cm) sin (3x – 6t)
wave 2: y(x, t) = (3 cm) sin (4x – 12t)
wave 3: y(x, t) = (4 cm) sin (5x – 11t)
where x is in meters and t is in seconds. Of these waves:
a) wave 3 has the greatest wave speed and the greatest maximum transverse string speed
b) wave 2 has the greatest wave speed and wave 3 has the greatest maximum transverse string speed
c) wave 2 has the greatest wave speed and wave 1 has the greatest maximum transverse string speed
d) wave 3 has the greatest wave speed and wave 2 has the greatest maximum transverse string speed
e) wave 1 has the greatest wave speed and the greatest maximum transverse string speed
7- The end point of a spring oscillates with a period of 3.3 s when a block with mass m is attached
to it. When this mass is increased by 1.6 kg, the period is found to be 7.1 s. Find m.
m
k
m
3.3  2
k
m  1.6k
7.1  2
k
T  2
Therefore:
7.1
m  1.6k

3.3
m
Physics 2130
Midterm Examination
Spring 2006
ID #:
Name:
m  1.6k
 7.1 
 m  0.44kg

 
m
 3.3 
2
8- Two sinusoidal waves, identical except for phase, travel in the same direction along a string,
producing a net wave y’ (x, t) = (1.6 mm) sin(25x - 5.8t + 0.76 rad), with x in meters and t in
seconds. What are (a) the wavelength of the two waves, (b) the phase difference between them,
and (c) their amplitude ym, and the transverse acceleration of a medium element along the path of
the waves?
y1  y m sin( 25 x  5.8t )
y 2  y m sin( 25x  5.8t   )
y   y1  y 2  2 y m cos( / 2) sin( 25x  5.8t   / 2)
2 2

 0.25m
k
25
a)

b)
 / 2  0.76    1.52rad
c) 2 ym cos(0.76rad )  1.6mm  ym  1.1mm
d)
a   2 y  5.82 (1.6) sin( 25x  5.8t  0.76) mm / s 2
9- A sound wave of the form s = sm cos(kx – ωt + φ) travels at 343 m/s through air in a long
horizontal tube. At one instant, air molecule A at x = 2.000 m is at its maximum positive
displacement of 6.00 nm and air molecule B at x = 2.070 m is at a positive displacement of 2.00
nm. All the molecules between A and B are at intermediate displacements. What is the frequency
of the wave?
v

k
Name:
Physics 2130
Midterm Examination
Spring 2006
ID #:
6nm  6nm cos( 2k  t   )
cos( 2k  t   )  1
2k  t    2n, n  0,1,2...
Therefore
 t    2k  2n, n  0,1,2...
2nm  6nm cos( 2.07k  t   )
cos( 2k .07  t   )  0.3333
2.07k  t    2n  1.23rad , n  0,1,2...
Substitute for  t   from above to get:
2.07k  2k  1.23rad
Or
0.07k = 1.23 rad or k=17.57
  vk  (343)17.57  6027rad / s
f   /( 2 )  959 Hz