Length Estimation

An experiment was carried out to determine the parameters of a bar with a specific target pitch. The following text outlines the experiment background, procedure, and results.

Background

The pitch of a vibraphone bar is determined by its size. A longer bar produces a lower tone. For this experiment, the target note is B4, 493.9 hz.

Procedure

The following tools and inputs are required for this experiment:

• Fusion 360
• idiophone-bar.py

Binary search trial and error can be used to determine the length of the bar that produces the target frequency. The script requires input for length, width, height, and tone. The following parameters remain constant:

Height:	2.25 in
Width:	0.50 in
Tone:	0.8

Note: When running the script, these parameters will be set as default. Only modify the length value for this experiment.

The experiment is carried out as follows:

1. Run the script in Fusion 360
2. Input a length value
3. Run modal analysis
4. If the resulting fundamental is not close to the target frequency, adjust the length accordingly

Results

I made some lucky guesses and used a binary search approach initially. The trials are recorded in the following table:

Guess #	Length Guess (mm)	Frequency (hz)
1	350.00	444.7
3	340.00	466.5
4	331.00	492.1
5	330.50	493.6
6	330.45	493.7
7	330.40	493.9
2	330.00	495.1

The target length to be used in the next eperiment is 330.4 mm.