Question

A) 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 3.60 grams per meter, and that all have a tension of 270 N.
If you want one of the strings to have a fundamental frequency of 440 Hz, how long should you make it?
_______ m

B)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 3.60 grams per meter, and that all have a tension of 270 N.
If you want another of the strings to have a fundamental frequency of 330 Hz, how long should it be?
_______ m

Answer 1

The frequency of a wave in string can be represented as,

f = v / 2l

Here, v is the velocity of the wave.

v = (T / )1/2

Here, T is the tension of the string, and is mass per unit length of the string.

So, f =

a) Here, = 3.6 g/m

= 3.6 × 10-3 kg/m

T = 270 N

f = 440 Hz

Therefore, l = 0.311 m

b) Here,

= 3.6 g/m

= 3.6 × 10-3 kg/m

T = 270 N

f = 330 Hz

Therefore, l = 0.415 m