Transcript Shrieking Rod - IYPT Archive

Shrieking Rod
Prof. Chih-Ta Chia
Dept. of Physics NTNU
Problem # 13
 Shrieking rod
 A 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
Cl 
Longitudinal wave speed
E: Young’s Modulus
E

m
Ct 

Torsional wave speed
m: Shear Modulus
1 2
Passion Ratio :     1
2
fl

ft
Young’s Modulus
Stress: S
F
S 
A
Longitudinal Strain: St
Young’s Modulus: E
l
St 
l
S
Y 
St
Stress, Strain and Hook’s Law
L
Strain 
L
Hook’s Law
F
Stress 
A
Stress is proportional to Strain.
F
L
Y
A
L
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.
F
A
Shear Modulus: m m  Shear Stress 
x
Shear Strain
L
F
L
m
A
L
Resonance : When Clamped in the Middle
f nl
f nt
Cl
 2n  1
2L
Ct
 2n  1
2L
n  0, 1, 2, 3, 
Speed of wave in Rod
Flexural Vibrations
Equation of Motion : (Length L and radius a)
 y
 y
c
 2
4
x
t
4
2
l
2
2
1
2
    y dA
A
2
cl is the velocity of longitudinal waves in an
infinitely long bar.
Y
2
cl 

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.