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