The fundamental frequency of a vibrating string is f₁. If the tension in the string is decreased by 50% while the linear density is held constant, the fundamental frequency becomes A) 0.5f₁. B) 0.7f₁. C) 0.9f₁. D) f₁. E) None of these is correct.

Question

Quizplus · Accepted Answer

The fundamental frequency of a vibrating string is given by:
fS1U1B0 = (1/2L) * sqrt(T/μ)
where L is the length of the string, T is the tension, and μ is the linear density of the string.
When the tension is decreased by 50%, the new tension becomes T/2. The frequency of vibration with the new tension is given by:
f'S1U1B0 = (1/2L) * sqrt(T/2μ)
Dividing the two equations, we get:
f'S1U1B0/fS1U1B0 = sqrt(T/2μ) / sqrt(T/μ) = 1/sqrt(2)
f'S1U1B0 = (1/sqrt(2)) * fS1U1B0
f'S1U1B0 = 0.707fS1U1B0
Therefore, the fundamental frequency is decreased by a factor of 0.707 or approximately 0.7. The answer is therefore B.

The Fundamental Frequency of a Vibrating String Is F1

The Fundamental Frequency of a Vibrating String Is F₁