Report for Experiment #14
Standing Waves
Hannah Wilker
TA: Luning Yu
13 May 2020
Abstract
This lab focused on standing waves in two different mediums: a string and in air. Investigation 1 looked at
standing longit
...
Report for Experiment #14
Standing Waves
Hannah Wilker
TA: Luning Yu
13 May 2020
Abstract
This lab focused on standing waves in two different mediums: a string and in air. Investigation 1 looked at
standing longitudinal waves in a string, where the goal was to find the mass per unit constant of the string
by measuring the wavelength of the standing waves at different tensions, the tension of the string
changing the speed of the wave. The mass per unit constant was found to be 0.316 ± 0.025 g/m, which
was in agreement with the theoretical value of 0.32 g/m. Investigation 2 by contrast looked at sound
waves in air, which are transverse. Using a tuning fork, a sound wave was generated in the air column. By
measuring the height of the air column at the maximum intensities, we were able to calculate a
wavelength for that frequency. By graphing wavelength versus the inverse frequency, the slope of 347.3 ±
16.8 m/s was found to be the measured velocity in air, which agreed with the theoretical value of 343 m/s.Introduction
Experiment 14 is all about standing waves. Waves are an important phenomenon in science as they
are responsible for the transfer of energy but not matter. Waves can travel in many different mediums
including water, air, and solids. All waves obey the following relationship, their velocities are always
equal to the frequency times the wavelength
v=
λT
=fλ
(1)
In this lab we looked at waves that were fixed on one end and controlled by an oscillator on the other.
The fixed end causes a deflection of wave oscillation, and at certain frequencies and wavelengths, the
string can appear to be completely still and at a fixed amplitude. These are called standing waves. We can
produce standing waves with different wavelengths by varying velocity. For this experiment with a fixed
string, the wavelength is given by Equation 2:
λ
n=
2 L
n
(n=1,2,3…)
(2)
In this case, n is equal to the number of nodes (halfway points between the max amplitudes, or where
the string does not appear to move at all) subtracting 1. In Investigation 1, we will be changing the tension
in the string by varying the mass in the pail:
F
s=mg
(3)
This change in mass (and therefore change in tension) is what changes the velocity of the wave and
therefore the wavelength as frequency is held constant, according to Equation 4:
V
string=√Fμs
(4)
Where μ is the mass per unit of the string itself. By combining Eq. 4 with Eq. 2 and 1, we can see that
while the wavelength will change as all masses are added, if the mass is not a certain value a standing
wave will not appear as the velocity has not produced a wavelength that has a node at the deflection point.
In Investigation 1 we graph the velocity squared vs. tension in the string to determine the mass per unit
value of the string and compare it to the theoretical value. All of this is done by manipulating the mass of
the pail and measuring the length between adjacent nodes when a standing wave appears for n = 2-10.
V
string
2
=
F
s
μ
→ μ=
1
slope for V string 2 vs . Fs
(5)
For Investigation 2 we look at standing waves in the air versus on a string. Sound waves are
transverse, as opposed to waves on a string that are longitudinal. So instead of Eq. 2, the wavelength of a
standing wave with n + 1 nodes is given by Eq. 6 below:
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