ASTM E1876

Acoustic Frequency to Elastic Modulus

Input units are important.

Input linear dimensions using inches.

Input mass in grams.

Input frequency in Hertz (inverse seconds).

Assume a rectangular bar using width, length, and thickness (inches).

ff = flexural frequency

m = mass

b = width

L = length

t = thickness

T = correction factor

The correction factor can only be used if L/t ≥ 20!

E = Young's modulus

            
frequency Hertz

mass grams

width inches

length inches

thickness inches

error thickness inches

Elastic Modulus GPa (gigaPascals)

error Modulus GPa (gigaPascals)

            
Reference: https://www.astm.org/e1876-21.html

ASTM E1876-21: Standard Test Method for Dynamic Young's Modulus,

Shear Modulus, and Poisson's Ratio by Impulse Excitation of Vibration

https://en.wikipedia.org/wiki/Impulse_excitation_technique 

Elastic Modulia (GPa)
     13, lead
     68, aluminum annealed
     69, aluminum alloy 6061-T6
     72, aluminum alloy 7075-t6
    110, copper annealed
117-130, copper alloy 110
    115, bronze 316
    117, brass 360
    110, brass 260
    179, nickel alloy 400
    180, nickel alloy 200
190-210, 1080 steel
193-200, 314 stainless steel

For data collection, suggest high- quality directional-microphone, such as the USB Rode Video Mic NTG on a good boom arm, located directly above the sample's end.

For software, Visual Analyzer for PC (free 32-bit) and SpectraPlus-SC (free trial, pay later) have great "peak frequency" meters.

PhyPhox on iPhone and Google give passable results.

Suggest cross-calibrating with tone generators and/or tuning forks.

JQuinn 6/13/2022