Answer:
The new fundamental frequency is doubled! That is, new fundamental frequency = 134 Hz
Explanation:
The frequency (f) of vibration of stringed instruments is related to the Tension (T) in the spring by the relation
fₙ = (n/2L)√(T/μ)
where n = 1,2,3,4...
For fundamental frequency, n = 1
L = length of the string
T = tension in the string
μ = linear density
So, if all the other parameters are constant,
fundamental frequency is proportional to the square root of tension in the string
f ∝√T
f = k√T
k = constant of proportionality
k = f/√T
Let the initial fundamental frequency and tension be f₁ and T₁ respectively
f₁ = 67 Hz, T₁ = ?
k = 67/√T₁
Let the new fundamental frequency and tension be be f₂ and T₂ respectively
f₂ = ? But, T₂ = 4T₁
f₂ = k√T₂ = k√(4T₁) = 2k√T₁
But, k = 67/√T₁
f₂ = 2× (67/√T₁) × √T₁ = 2 × 67 = 134 Hz
Hence the new fundamental frequency is doubled!.
