PASCO WA-9867, Instruction Manual

Page: 24 / 32

Sine Wave Generator Resonance Tubes
24
®
Further Investigations
1. Set the frequency to 230 Hz, and extent the tube to 120 cm. Without changing the frequency,
slowly shorten the tube until you hear resonance. Adjust the tube length back and forth across
the resonance to locate the position of the node. Record the position of the node (which is the
length of the tube).
2. Without changing the driving frequency, continue to shorten the tube until you hear resonance
again. Record the position of this node.
3. The distance between the two resonance positions (the distance between adjacent nodes) is
1
⁄
2
λ
. Why?
4. Calculate the wavelength from the distance between the nodes. From this wavelength and the
frequency of the Sine Wave Generator, calculate the speed of sound. How does it compare
with your earlier value?
5. Draw a companion sketch of the waveform diagram on page 22, showing two nodes and the
same frequency. Remember that there must be a node at the closed end and an anti-node at the
open end. Hint: the tubes in the two drawings should not be the same length, but the
wavelengths are the same.
Part II:
Open and Closed Tubes of Fixed Length
Theory
A resonating tube with both ends open will always have an anti-node at either end, and at least
one node in between. The number of nodes is related the wavelength and the harmonic. The first
harmonic (or fundamental) has one node, the second harmonic has two, etc., as shown here:
At higher harmonics, the frequency is higher and the wavelength is shorter (length of tube does
not change).
Procedure
1. Slide the inner tube all the way out, and separate it from the outer tube. Use only the outer
blue tube with two open ends.
L
First Harmonic
L = 1/2
λ
Second Harmonic
L =
λ