PASCO WA-9867 Sine Wave Generator User Manual
Page 23
Model No. WA-9867
Experiment 2: Resonance Tubes
23
®
2. Extend the tube to 120 cm. Set the Sine Wave Generator frequency to 50 Hz, and turn up the
amplitude to a reasonable level.
3. Slowly increase the frequency using the coarse (1.0) knob, and listen for resonance. When you
are within a few hertz of the fundamental frequency, the loudness off the sound will increase
noticeably. (You will hear this resonance before the frequency reaches 100 Hz.) Using the
coarse knob, adjust the frequency up and down across the resonance. Listen carefully to
determine at what frequency it is loudest. Try to determine the resonance frequency to the
nearest 1 Hz. Record the tube length and frequency in a table.
4. Decrease the length of the tube to 110 cm and repeat the previous step. Take data at 10 cm
intervals down to a length of 50 cm. (The resonance frequency will eventually exceed 100
Hz.)
5. Make a graph of Tube Length versus Inverse Frequency (L vs.1/f ). Note that the horizontal
axis is the inverse of frequency.
6. Find both the slope and the y-intercept of the best-fit line through this data.
7. From Equation 3 we see that the slope of the graph is:
Use the slope from your graph to calculate the speed of sound in air. Estimate the uncertainty.
8. The actual speed of sound depends on the temperature of the air:
where T is the temperature of the air in degrees Celsius. Measure the air temperature and
calculate the actual speed of sound.
9. Compare your measured speed of sound from step 7 to the actual speed of sound. Calculate
the percent deviation.
10. On your graph of L vs. 1/f, why isn't the y-intercept zero? Is the intercept negative?
A negative intercept indicates that the effective length of the tube is longer than the actual
length. The anti-node at the open end of the tube is actually formed past the end, slightly
outside the tube. This phenomenon is called the “end effect”. The extra end-effect length is
proportional to the diameter of the tube, and can be empirically represented as
End Effect = 0.3 × Diameter of Tube
Measure the diameter of the tube and use this equation to calculate the end effect. How does
this value compare with the y-intercept of your graph?
Slope
¼ v
=
v 331
m/s
0.6 T
+
=
% Deviation
Measured
Actual
–
Actual
---------------------------------------------
100%
Ч
=