- #1
gasar8
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We've got a 0,5m string attached to a frame and has its own fundamental frequency at 440Hz. We cool our system for 15°C. What is the proper frequency now?
String length l=0,5m
String section S=0,02 mm^2
String density ρ=7800 kg/m^3
Young module E=2*10^5 N/mm^2
Fundamental frequency ν=440Hz
ΔT= -15°C
α(string)=1,2*10^-5 /K
α(frame)=1,7*10^-5 /K
Δl/l=F/(ES)+α⋅ΔT
I assume that F(string)=F(frame) and Δl(string)+Δl(frame)=0, so:
F/(ES) +α(string) ΔT + α(frame) ΔT=0
From this equation I get F=1,74N, but I can't imagine what this number means?
c=√(E/ρ) = 5063 m/s is this equal to √(F/(ρS))? What is this force? (4000N)
String length l=0,5m
String section S=0,02 mm^2
String density ρ=7800 kg/m^3
Young module E=2*10^5 N/mm^2
Fundamental frequency ν=440Hz
ΔT= -15°C
α(string)=1,2*10^-5 /K
α(frame)=1,7*10^-5 /K
Homework Equations
Δl/l=F/(ES)+α⋅ΔT
I assume that F(string)=F(frame) and Δl(string)+Δl(frame)=0, so:
F/(ES) +α(string) ΔT + α(frame) ΔT=0
From this equation I get F=1,74N, but I can't imagine what this number means?
c=√(E/ρ) = 5063 m/s is this equal to √(F/(ρS))? What is this force? (4000N)