Prof. Williams
2.10.2020
Resonance in Air Columns
Purpose statement:
The purpose of this lab was measuring the points that resonance is happening. Within those
measurements, we were able to calculate the wave speed for those frequencies. We were also able
to calculate an unknown frequency with calculating the speed of the sound from the room
temperature and the wavelength that was measure from the difference between two consecutive
resonance points.
V. CALCULATIONS
A. Compute the average length for the resonance lengths for each line of the data table.
f=390.9 Hz
Avg.L1=(9.1+10.2+9.2)/3=9.5 cm
Avg.L2=(51.6+52+57.9)/3=53.83 cm
f=440 Hz
Avg. L1=18.4 cm
Avg.L2=57.83 cm
Unknown f: #8
Avg. L1=8.05 cm
Avg. L2=43.05 cm
B. For a single frequency subtract the average L, from L and solve for the wavelength.
Multiply the wavelength by the frequency to compute the speed of the wave. Repeat for
each frequency.
f=390.9 Hz
Avg.L1-Avg.L2=53.83-9.5=44.33 cm= Avg.Wavelength/2
v=lf=(88.66/100)*390.9 = 346.572 m/s
f=440 Hz
Avg.L1-Avg.L2=57.83-18.4=39.43 cm= Avg.Wavelength/2
/2=39.43cm -> =39.43*2=78.86 cm
v=Af=(78.86/100)*440 = 347.013 m/s
Unknown f:#8
Avg.L1-Avg.L2=43.05-8.1=34.95 cm= Avg. Wavelength/2
/2=34.95 cm ->1=34.95*2=69.90 cm
C. Compute the average speed of sound for the three frequencies.
The average speed of sound for the first two frequencies:
Vavg.=(346.572+347.013)/2=346.793 m/s
V of sound from the room temp.= v = vo + 0.6T
v=331.3+0.6*23.11= 345.17 m/s
Percent difference of the speed of the sound from f1,f2 and v of the sound from room temp.
("#$)
CO.+,#'(-..+
D. Calculate the speed of sound from knowing the air temperature and the equation in the
last paragraph of the Background information.
v = vo + 0.6T
v=331.3+0.6*23.11= 345.17 m/s
E. Calculate the percent difference for the speed of sound values calculated in parts C, D.
and F.
la-bI 347.013 - 346.752 (%)p *100 * 100 = 0.12727% (a+b) (347.013 + 346.752) 2 2
F. Determine the frequency of the unknown tuning fork.
v=1f
f=v/=345.17/(69.90/100))= 493.801 Hz
!
VI. CONCLUSIONS/QUESTIONS
A. Discuss the possible sources of error in this experiment.
-For measuring the resonances for the given frequencies, even though the procedure was done
quick enough, the frequencies had dropped down by a few decimals during measuring resonances
-Error in reading the exact value on the ruler for the resonance.
-Not setting the plunger at a point where the resonance exactly is.