Question

An Aeolian harp (named after Aeolus, the Greek god of the wind) consists of several strings fixed to a frame or a sounding box. The device is simply placed outside, and the strings are played randomly by the wind. You decide to make such a harp out of strings that all have a mass per unit length of 2.40 grams per meter, and that all have a tension of 350 N. If you want one of the strings to have a fundamental frequency of 440 Hz, how long should you make it

Answer 1

Answer:

0.434 m

Explanation:

We are given that

Mass per unit length=$\mu=\frac{m}{l}=2.4 g/m=2.4\times 10^{-3} kg/m$

1 kg=1000 g

Tension=350 N

Fundamental frequency=f=440 Hz

We have to find the length you should make it.

We know that

$l=\frac{1}{2f}\sqrt{\frac{T}{\mu}}$

Using the formula

$l=\frac{1}{2\times 440}\times\sqrt{\frac{350}{2.4\times 10^{-3}}}$

l=0.434 m

Hence, you should make it 0.434 m long.