# Vibrating Strings

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```Vibrating Strings
Purpose: To verify that strings do exist and that they will, in fact, vibrate.
Apparatus
Mass balance
String
2-meter stick
string driver
rod and clamp
hanging mass
Theory
One can set up standing waves on a string which is fixed at both ends by vibrating it at just the right
frequency. At the right frequency, waves travelling down the string will interfere constructively
with each other and with waves travelling in the opposite direction.
In fact, there are a whole set of frequencies which will work: a fundamental frequency f and
its harmonics, 2f, 3f, etc. Any frequency that results in a standing wave is given by
f 
N
2L
FT

(Eq. 1)
In the above equation, f is the frequency (Hertz, or 1/s) of the vibration, N is a positive
integer indicating the number of antinodes, L is the length of the vibrating string (meters)
from the driver to the horizontal rod, FT is the force of tension on the string (Newtons), and
μ is the linear mass density of the string (kg/meter). Linear mass density is the length of
the string being used divided by the mass of the string being used.
Because L, T, and μ are constants, Eq. 1 may be expressed as a linear equation in the form
y=mx.
 1
f  
 2L
FT 
N
 
You will set up standing waves at different frequencies, graph them as a linear equation,
and use the above equation to figure out what the linear mass density of the string ought to
be. Then, you'll compare it to the actual linear mass density, and see if the theory works.
The stated value of the linear mass density of your string is 1.5 x 10-3 kg/m. Perform a
percent error calculation to see how close you are to the stated value.
```