A harp consists of several strings fixed to a frame or a sounding box. The devic

Question

A harp 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 2.00 grams per meter, and that all have a tension of 300. N.

(a) If you want one of the strings to have a fundamental frequency of 440 Hz, how long should you make it? (m)

(b) If you want another of the strings to have a fundamental frequency of 330 Hz, how long should it be? (m)

Explanation / Answer

a) suppose length of string L then

wavelength = 2L ( for funamental)

linear mass density = 2 g / m = 0.002 kg/m

speed of wave = sqrt(T / linear mass density) = sqrt(300 / 0.002) = 387.3 m/s

Frequency = speed / wavelength

440 = 387.3 / 2L

L = 0.44 m

b) speed will be same.

Frequency = speed / wavelength

330 = 387.3 / 2L

L = 0.59 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.