The note produced by a stretched string has a fundamental frequency of 400Hz. If the length of the string is doubled while the tension in the string is increased by a factor of 4, the frequency is
200Hz
400Hz
800Hz
1600Hz
Explanation
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Solution 🔥
If you're still confused or doubting 400Hz✅ to be correct, I'm sure my soln will make you believe.......
F ∞ 1/L.............(Ω)
F ∞ √T..............(π)
Combining (Ω) & (π)
F ∞ 1/L•√T
F = k√T/L
When F=400Hz, T=1N, L=1m
k = FL/√T ==> (400×1)/√1
k = 400
When L=2m, T=4N F=?
F = k√T/L ==> 400×√4/2
F = 200√4 = 200×2 = 400Hz✅
Problem Solved!!!
Now you believe 400Hz is correct 😅
i think this is where most of us are getting it wrong;
when they say tension is increased by a factor of 4 it means √4T not 4√T
i hope it helps
The answer given is correct.
F=1/2L√T/K
F1×2L1/√T1=√K...(1)
F2×2L2/√T2=√K..(2)
Making √K=√K
F1×2L1/F2×2(2L1)=√T1/√T2
400×2L1/F2×4L1)=√1/√4
800L1/F24L1=1/2
800/F24=1/2
800×2/4=F2
1600/4=F2
F2=400hz
