Sample Final (1113)
1. Transverse Standing Waves, A resonance condition is reached as
2.00 m
shown in the right figure.
(a) What is the wavelength of the standing wave? (4 points)
(b) If the frequency of the wave is 120 Hz, what is the speed of the wave?
(4 points)
(c) What is the physical meaning of wave speed for a standing wave? (4 points)
(d) Furthermore, the speed can be changed by adding/reducing the mass (so does the tension) in the
mass holder. The relationship between the wave speed, v, and the tension applied on the string,
Ten
Ten, is v 
, where  is linear density
Ten (N)
v (m/s)
v2 (m2/s2)

1.00
44.3
of the string. Measured data of Ten and v
1.98
62.3
are listed in the following table. Find 
2.94
75.9
(with units) using the graphic paper
3.95
88.0
provided ( will be the slope of your plot).
4.92
98.2
(10 points)
6.00
108.4
(e) If the true value of  is 5.15x10-3 g/cm, find your percentage error. (5 points)
(f) Find the mass needed to produce 10 loops. (10 points)
2. Torque and Static Equilibrium, masses of 100 g and 300 g are placed at 0.0 cm and 90.0 cm
points of a meter stick respectively. The meter stick is uniform and has a mass of 100 g. If a
normal force is applied at certain position that the meter stick achieves a balance.
a) Draw a diagram of the forces on the meter stick. (11 points)
b) Calculate the magnitude of the normal force. (11 points)
c) Calculate the position of the normal force. (11 points)
3. (30 points) Simple Harmonic Motion and Hook’s Law, A
plot of T2 against mass added madd is shown in the right
figure. The dots are the experimental data and the solid line
is the best fit based on the following equation. Find the
spring constant, k, and the mass of the mass holder, mholder,
from the PLOT and the equation.
2
T2 (sec 2)
4 2 m holder
4 2
T 
m add 
k
k
2
3
1
0
0
40 80 120 160 200 240 280
mass (g)
(Bonus, 10 points) In problem 3, if we need an oscillation with
1 Hz, how much mass needed to add to the holder?