The fundamental frequency of a vibrating string is f₁. If the tension in the string is increased by 50% while the linear density is held constant, the fundamental frequency becomes A) f₁. B) 1.2f₁. C) 1.5f₁. D) 1.7f₁. E) 2f₁.

Question

Quizplus · Accepted Answer

The fundamental frequency of a vibrating string is given by:f = (1/2L) * sqrt(T/μ)where:f is the fundamental frequencyL is the length of the stringT is the tension in the stringμ is the linear density of the stringIf the tension in the string is increased by 50%, then the new tension becomes:T' = 1.5TSubstituting this into the equation for the fundamental frequency, we get:f' = (1/2L) * sqrt(1.5T/μ)= (1/2L) * sqrt(1.5) * sqrt(T/μ)= 1.2 * (1/2L) * sqrt(T/μ)= 1.2fTherefore, the fundamental frequency becomes 1.2f.

The Fundamental Frequency of a Vibrating String Is F1

The Fundamental Frequency of a Vibrating String Is F₁