Vibration of a wine glass
A model for the vibrations of a wine glass is
x¨ + λx˙ + (ω^2)x = 0
Suppose that when struck the wine glass vibrates at 660 Hz (about the second E above middle C on a piano). Show that. √(4ω^2 − λ^2) = 2640π
If it takes about 3 seconds for the sound to die away, and this happens when
the original vibrations have reduced to 1/100 of their original level, show that
λ =(2 (log 100))/3
and hence that λ = 3.07 and ω = 4.15 x10^3(both to three significant figures).
The glass can stand deforming only to x nearly equal to 1. A pure tone at 660 Hz is produced and aim at the glass,forcing it at its natural frequency so that the vibration are now modelled by x¨ + λx˙ + (ω^2)x = cos(1320pi t)(10^((D/10)-8))/3
How large should the sound be in order to shatter the glass?
Re: Vibration of a wine glass
Quote:
Originally Posted by
kanezila 
A model for the vibrations of a wine glass is
x¨ + λx˙ + (ω^2)x = 0
Suppose that when struck the wine glass vibrates at 660 Hz (about the second E above middle C on a piano). Show that. √(4ω^2 − λ^2) = 2640π
If it takes about 3 seconds for the sound to die away, and this happens when
the original vibrations have reduced to 1/100 of their original level, show that
λ =(2 (log 100))/3
and hence that λ = 3.07 and ω = 4.15 x10^3(both to three significant figures).
The glass can stand deforming only to x nearly equal to 1. A pure tone at 660 Hz is produced and aim at the glass,forcing it at its natural frequency so that the vibration are now modelled by x¨ + λx˙ + (ω^2)x = cos(1320pi t)(10^((D/10)-8))/3
How large should the sound be in order to shatter the glass?
Well, what have you tried? What is the general solution to the homogeneous equation?
CB
