Laboratory #4: Vibrational Modes of a Metal Bar
Objective:
In this lab we will measure the bending modes of an aluminum bar. We will determine the overtone series and the dependence of the frequencies on the length of the bar. The results are quite different from a vibrating string.
Equipment:
Diagram:
Instructions:
DATA:
Bar #1. Length of bar =
Mode: |
1 |
2 |
3 |
Frequency [Hz] |
|||
Position of node from bottom of bar. [cm] |
Bar #2. Length of bar =
Mode: |
1 |
2 |
3 |
Frequency [Hz] |
|||
Position of node from bottom of bar. [cm] |
Bar #3. Length of bar =
Mode: |
1 |
2 |
3 |
Frequency [Hz] |
|||
Position of node from bottom of bar. [cm] |
Questions:
Length of bar, L |
f2/f1 |
f3/f1 |
Length of bar, L |
Fundamental, f1 |
L*f1 |
f1*Ö L |
f1*L2 |
Length of bar, L |
2nd overtone, f2 |
L*f2 |
f2*Ö L |
f2*L2 |
Length of bar, L |
3rd overtone, f3 |
L*f3 |
f3*Ö L |
f3*L2 |
From these tables, how does frequency depend on length? Do you have the same dependence for each overtone?