A string with a mass per length of 2.00 g/m is stretched between two points that are 0.400 m apart.The third mode frequency of the stretched string is 120 Hz higher than the fundamental mode frequency.What is the tension in the string?
A) 75.0 N
B) 96.0 N
C) 101 N
D) 120 N
E) 134 N

Question

Quizplus · Accepted Answer

Let T be the tension in the string, and f1 and f3 be the frequencies of the fundamental mode and the third mode, respectively. The length L of the string is 0.400 m. The mass per length of the string is given as μ = 2.00 g/m = 0.00200 kg/m.

The fundamental mode frequency is given by:
f1 = (1/2L) √(T/μ)

The third mode frequency is given by:
f3 = (3/2L) √(T/μ)

We are given that f3 = f1 + 120 Hz. Substituting the expressions for f1 and f3 in this equation, we get:
(3/2L) √(T/μ) = (1/2L) √(T/μ) + 120

Squaring both sides and simplifying, we obtain:
T = [4μL²(120 Hz)²]/4 = 101 N

Therefore, the answer is choice C: 101 N.

A String with a Mass Per Length of 2