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Algebra - "Quartz Tuning Fork" Watch
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
Hint: try working this out algebraically. The changes are small and prone to rounding issues.
αQuartz = 0.59 × 10-6/°C
Not sure if the following equations are useful, but my topic of study right now is based on thermal expansion, as well as calculations based on heat energy (Q = mcΔT).
ΔL = αL0ΔT (linear thermal expansion)
If a body has length L0 at temperature T0, then its length L at a temperature T = T0 + ΔT is:
L = L0 + ΔL = L0 + αL0ΔT = L0(1 + αΔT)
Q = mcΔT
This question appears to me on a topic that I haven't touched so far in my Physics class; however, I know that the topics I am studying is interconnected with this question somehow. From what I read from the question, I concluded that frequency = 1/√length but I don't know how to incorporate that into an equation in which I can find a "ratio." I am stuck here and do not know how to further approach this problem.
Homework Statement
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
Hint: try working this out algebraically. The changes are small and prone to rounding issues.
αQuartz = 0.59 × 10-6/°C
Homework Equations
Not sure if the following equations are useful, but my topic of study right now is based on thermal expansion, as well as calculations based on heat energy (Q = mcΔT).
ΔL = αL0ΔT (linear thermal expansion)
If a body has length L0 at temperature T0, then its length L at a temperature T = T0 + ΔT is:
L = L0 + ΔL = L0 + αL0ΔT = L0(1 + αΔT)
Q = mcΔT
The Attempt at a Solution
This question appears to me on a topic that I haven't touched so far in my Physics class; however, I know that the topics I am studying is interconnected with this question somehow. From what I read from the question, I concluded that frequency = 1/√length but I don't know how to incorporate that into an equation in which I can find a "ratio." I am stuck here and do not know how to further approach this problem.