When a tuning fork of frequency 262 Hz is struck, it loses half of its energy after 4s. What is the decay time t ?

Options

A. 3 s
B. 4.5 s
C. 5.77 s
D. 6.28 s

Answer

C

Explanation

`E=E_(0)e^(-t//tau)` where `tau` is the decay time
(Generally we use `lamda " for " tau)`
At time `t=4 s, E=(E_(0))/(2)`
`therefore (E_(0))/(2)=E_(0)e^(-4//tau)`
`therefore (1)/(2)= e^(-4//tau) therefore 2 =e^(4//tau)`
Taking logarithms on both sides, we get
`therefore (4)/(tau)= log_(e )2`
`therefore tau=(4)/(log_(e )2)=(4)/(2.3026xx0.3010)=5.77s`