Shrieking Rod

Prof. Chih-Ta Chia

Dept. of Physics NTNU

Problem # 13

Shrieking rodA metal rod is held between two fingers

and hit. Investigate how the sound produced depends on the position of holding and hitting the rod?  

Vibration in rod? How did you create vibrations in the rod? Three type of vibrations are created simply by hitting

the rod: Longitudinal, torsional and flexural vibrations. Longitudinal and Flexural vibrations are most likely to

last longer, but not the torsional vibrations. What are the resonance conditions for these three

vibrations? What are the speeds of these three vibrations that

travel in the rod. How to determine the wave velocity?

Vibration of Rod?

What is the damping effect on the longitudinal and vibrations? Hitting position dependence? Time dependence?

Longitudinal wave damping and flexural vibration damping? Which one is damped fast?

Cylindrical Rod : Longitudinal and Torsional wave

E

Cl Longitudinal wave speedE: Young’s Modulus

Torsional wave speed: Shear Modulus

tC

Passion Ratio : 12

1 2

t

l

f

f

Young’s Modulus

A

FS

Stress: S

Longitudinal Strain: Stl

lSt

Young’s Modulus: EtS

SY

L

LStrain

A

FStress

Hook’s Law

L

LY

A

F

Stress is proportional to Strain.

Stress, Strain and Hook’s Law

Shear Modulus The shear modulus is the elastic modulus we use for the deformation which takes place when a force is applied parallel to one face of the object while the opposite face is held fixed by another equal force.

L

L

A

F

Shear Modulus:

LxA

F

StrainShear

StressShear

Resonance : When Clamped in the Middle

L

Cnf l

nl 212

L

Cnf t

nt 212

3, 2, 1, 0,n

Speed of wave in Rod

Flexural VibrationsEquation of Motion : (Length L and radius a)

2

2

4

422

t

y

x

ycl

cl is the velocity of longitudinal waves in an infinitely long bar.

The radius of gyration is defined as above. For the circular rod, is half the bar’s radius. As for the square rod, is D/√12.

dAyA

22 1

Y

cl 2