VIBRATION OF A BAR

L/2 L/4L/2

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VIBRATION OF A BAR

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VIBRATION OF A BAR

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VIBRATION OF A BAR

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VIBRATION OF A BAR

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VIBRATION OF A BAR

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VIBRATION OF A BAR

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𝑭 =𝟑. 𝟎𝟏𝟏𝟐𝝅

𝟖 𝟏𝟐

𝒀

𝝆

𝑻

𝑳𝟐

This transverse vibration mode is the fundamental

The frequency F is Y is the young modulus = 69Gpa for Al

ρ is the bulk density = 2700kg/m3

for Al

T is the thickness = 0.00635m ¼”

L is the length of the bar = 0.355 for C4

VIBRATION OF A BAR

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All the transverse modes are expressed as:

𝑭 =𝝅

8 12

𝒀

𝝆

𝑻

𝑳23.0112, 52 , 72, … , 2𝒏 + 1 2, …

VIBRATION OF A BAR

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The ratios for the harmonics are:

0 1 2 3 4 5 6 Harmonic#

1 2.758 5.405 8.934 13.346 18.641 24.816 Ratio

The ratios of harmonics are not whole or rational numbers. Therefore, a solid bar will not

produce a “harmonious” sound.

MARIMBA – COMPARISON BETWEEN THEORETICAL VALUES AND ACTUAL MEASUREMENTS

F0

(Hz)

Just Scale

F0

(Hz)

Measured

261.63 261.70

327.03 327.00

392.44 392.30

523.25 523.50

C4

C5

E4

G4