Newbury Park High School - Physics
Lab: Waves on a String – The Sonometer
Purpose: Derive experimentally a formula for the fundamental frequency of
vibration of a string as a function of the length of the string and the tension
on the string, and the linear density of the string.
Leveling Knob
Pick-Up Coil
Tension Arm
Left Hand
Bridge
Part I: Length vs. Frequency, Tension and Linear Density held constant.
Procedures:
1. Put the yellow wire on the sonometer, adjust the knob on the left side
until the tension arm is level. (See fig.1)
2. Adjust the black bridges so that the left one is set at 10 cm and the
right hand one is set at 75 cm. This gives a length of 75-10 or 65 cm.
3. Make sure the pick-up coil is about in the center of the wire.
4. Using the plastic loop put a 1 kg mass on the tension hanger on slot 5
(furthest from the wire).
5. Turn the oscilloscope on. Once it finishes its automatic calibration
procedure turn on the frequency counter. To do this, press the
“selector” lever down 4 times until the word “Freq” appears at the
upper left of the screen. (See fig. 2)
6. Readjust the knob on the left to level the tension arm if needed.
7. Pluck the string to set it vibrating. Read the frequency on the
oscilloscope. To get the best reading, let the vibrations settle down
for a second or two before taking the reading. Repeat this several
times and take an average of the frequency readings and record them
on your data table.
8. Move the right hand black bridge 5 cm to the left to 70 cm and
repeat the steps to take a frequency reading.
9. Continue to vary the length by moving the right hand bridge in
increments of 5 cm until you have taken 8 readings.
Newbury Park High School - Physics
Selector Lever
Slot # 5
Right Hand Bridge
Tension Hanger Arm
Part II: Tension vs. Frequency, length and linear density constant.
Procedures:
1. Return the right hand black bridge to the 75 cm mark.
2. The 1 kg mass should be on the # 5 slot on the tension hanger. Again
make sure the tension hanger is level.
3. Pluck the string as before and record the average frequency of the
wire.
4. Move the 1 kg mass to the #4 slot on the tension hanger. Readjust
the knob on the left to level the hanger.
5. Pluck the string as before and record the average frequency of the
wire.
6. Continue in this manner, moving the mass to subsequent hanger slots
for a total of 5 readings (one for each slot).
Part III: Linear Density vs. Frequency, length and tension constant.
Procedures:
1. With the 1 kg mass on the # 5 slot, and the bridges set to 10 cm and
75 cm pluck the wire as before and record the frequency.
2. Using the micrometer, measure and record the diameter of the wire.
Take several measurements, each at a different spot on the wire.
Measure the diameter with the 1 kg mass on the #5 slot.
3. Change wires and repeat steps 1 and 2. Continue this until all five
wires have been tested.
Newbury Park High School - Physics
Calculations and Analysis:
1. Using Excel, create the following graphs. Length vs. Frequency,
Tension vs. frequency, and Linear Density vs. Frequency. In each case,
frequency is on the y axis.
2. Insert a trendline, and trendline equation for each graph.
3. Using the exponents from each graph, derive (experimentally) the
formula…
freq = kLxTyz
Where k = a constant x, y, and z are the
exponents from the trendline equations.
4. Calculate a percent error for each exponent.
5. Calculate the value of the constant k for your equation. Do this by
entering various data points, and taking an average. Calculate a
percent error for k. The actual equation is…
Frequency 
1
Tension
2Length Linear Density
Finding Linear Density ()
Wire diameter (measured):
0.590mm
 Radius = 0.295mm
Density of Steel (look up):
7800 kg/m3
Consider 1.00 m of wire…
1.00m
Linear Density 
kg
m
Volume of wire = (R2)(1.00m)
= [(0.295mm)(1m/1000mm)]2(1.00m)
=2.73x10-7m3
mass of 1.00 m wire = density x volume
= (7800 kg/m3)(2.73x10-7 m3)
= .002132 kg/m
This is the linear density (), the mass
per meter of the wire.