Many modern watches operate based on a small quartz tuning fork which
transduces a mechanical oscillation into an electrical signal. The frequency of the tuning fork is
inversely proportional to sqrt(l), with l being the length of the fork. If the watch keeps perfect time at
20 C, what is the fractional gain or less in time for a quartz tuning fork that is 6mm long at:

(a) 0 C
(b) 30 C
α Quartz = 0.59x10^6 /C

Question

Many modern watches operate based on a small quartz tuning fork which
transduces a mechanical oscillation into an electrical signal. The frequency of the tuning fork is
inversely proportional to sqrt(l), with l being the length of the fork. If the watch keeps perfect time at
20 C, what is the fractional gain or less in time for a quartz tuning fork that is 6mm long at:

(a) 0 C
(b) 30 C 
α Quartz = 0.59x10^6 /C