Download PHYSICS 2C

STANDING WAVES ON A STRING
OBJECTIVES:
The objectives are to investigate the vibration of a string and measure the relationship
between the  (density), tension (T), and the velocity of vibration (v). In particular we
will find:
1. Resonances occur only for certain values of the tension (T) in the string for a given
suspension length.
2. The relationship between the velocity of vibration on a string is given by:
v = (T/)1/2
APPARATUS:
 1 String vibrator
 1 mass holder and slotted masses
 1 meter stick (preferably 2 meter stick), clamps, pulley, support rods
 String with density = 0.159 gr/m.
DISCUSSION:
A wave can be created in a taught string when the string is vibrated
perpendicularly to its length. If a lateral vibration is forced at a point on a taught string, a
lateral wave propagates along the string from that point. The velocity of propagation is
given by the above formula.
Consider the situation where a string is tied to a vibrator at one end and the other
end passes over a pulley and is attached to a hanging mass (the distance between the
vibrator and pulley is L). When a wave is formed in the string at a frequency such that it
has an antinode at the vibrator and a node at the pulley, a resonance is created. In this
experiment changing the hanging mass can vary the tension and the vibrator control will
vary the frequency. A resonance is produced when the velocity of vibration in the string
allows an integral number of half wavelengths between the vibrator and pulley. The
proper adjustment of T and f will produce a resonance.
A standing wave requires an antinode at the vibrator and a node at the pulley.
The relationship between the wavelength and L is given by:
n (/2) + /4 = L; where n = 0,1,2,…
Since relationship among , , and v is given by:
v = (T/)1/2
and v = f . For a given L and , we can vary T and f until resonances are detected.
PROCEDURE (Measurement of density is optional):
1. Carefully measure 2 to 3 meters of string and measure the mass of it. Find the linear
density . Since this one value will be used in all our calculations, make several
measurements and zero the scale before each measurement.
2. Clamp the vibrator and the pulley at opposite ends of the table as the demonstration
set. Place a 20-gram mass on the loop.
3. Carefully measure the length of the string from the tip of the vibrator to the point at
the very top of the pulley where the string touches the pulley. Record this length L in
the data table.
4. Plug in the vibrator and find a frequency that is required to produce a standing wave
(the largest amplitude of vibration). Slowly increase the frequency until a standing
wave is formed and note the value of n (n will equal the number of nodes along the
length of the string). Enter the values for this first standing wave in the table. Now,
increase the frequency to form a few more standing waves at this tension.
5. Add 20 grams more mass on the mass holder. Readjust the frequency so that standing
waves are formed and enter the data in the table.
6. Add 20 grams more mass on the mass holder. Readjust the frequency so that standing
waves are formed and enter the data in the table.
7. Now calculate the experimental and theoretical vibration velocities.
Measurement
Mass
Length
Density ()
Mean  = _______________
Standard Error of the Mean: ______________
Note: Drop outliers if you believe that that will produce a more accurate measurement.
ANNALISYS:
1.How well do the theoretical values of the speed of waves in the string compare to the
measured values?
2. Can you explain any discrepancies between the theoretical and measured values of the
speed of wave in the string?
2
 = _______________________
Hanging Mass
(m)
Tension
(Newtons)
Frequency
(Hertz)
Number of
Nodes
Wavelength
(meters)
Experimental
Velocity (v = f)
(meters/second)
Theoretical
Velocity (v =
(T/)1/2 )
(meters/second)
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