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 the equation:

f = (1/(2L)) * sqrt(T/μ)

where f is the frequency, L is the length of the string, T is the tension in the string, and μ is the linear density of the string.

If the tension in the string is decreased by 50% while the linear density is held constant, the new tension is T/2. Therefore, the new frequency is given by:

f' = (1/(2L)) * sqrt((T/2)/μ)

f' = (1/(2L)) * sqrt(T/2) * sqrt(1/μ)

f' = (1/(2L)) * (sqrt(T)/sqrt(2)) * (1/sqrt(μ))

Since the linear density is held constant, 1/sqrt(μ) remains the same. Therefore, the new frequency is equal to:

f' = (1/(2L)) * (sqrt(T)/sqrt(2)) * (1/sqrt(μ))

f' = (1/(2L)) * (1/sqrt(2)) * f

f' = 0.7f

Therefore, the new fundamental frequency is 0.7 times the original frequency, which corresponds to choice B.

The Fundamental Frequency of a Vibrating String Is F1

The Fundamental Frequency of a Vibrating String Is F₁