Calculating Qf: Piano Key Frequency 256Hz Energy Dissipated in 1s

[Eric_meyers]

Homework Statement

"Systems typically exhibit an exponential decrease in their average stored energy of the form <E> = E$$_{0}$$ e^(-vt) ---- If a piano key of frequency 256 Hz is struck and its oscillation energy decreases to one half of its initial value in about 1 second what is the effective Qf of the system?

Homework Equations

Qf = w/v
<E> = E$$_{0}$$ e^(-vt)

The Attempt at a Solution

I need to find the energy dissipated and from the equation they gave me I put 1/2 (the energy the system has from its initial value after 1 second)

1/2 = e^(-v)

v = .693

Qf = 256/.693 = 369

I'm not quite sure if I did the dissipation energy equation correctly.

 

[Winzer]

$$Q=\frac{\omega}{v}=\frac{2 \pi f}{v}$$. Your numerator needs to be in angular frequency. Looks fine though.