Question

The least possible frequency of a string is its fundamental frequency. The fundamental frequency $n$ (in hertz) of a certain string on a violin is represented by $n=\sqrt{\frac{T}{0.0054}}$ , where $T$ is the tension (in newtons). The fundamental frequency of the string is $196$ hertz. What is the tension of the string? Round your answer to four decimal places

Answer 1

The tension of the string on the violin is 207.9444 newtons.

Step-by-step explanation:

The fundamental frequency of a string on a violin is given by the equation n = sqrt(T/0.0054), where n is the frequency in hertz and T is the tension in newtons. We are given that the fundamental frequency is 196 hertz, so we can set up the equation as follows:

196 = sqrt(T/0.0054)

Squaring both sides of the equation, we have:

38416 = T/0.0054

Multiplying both sides by 0.0054, we get:

T = 207.9444

Rounding to four decimal places, the tension of the string is 207.9444 newtons.