A steel piano string is 47.9 inches long. The diameter of the string 0.0421 inch

Question

A steel piano string is 47.9 inches long. The diameter of the string 0.0421 inches. When struck, this string produces the musical note, B, which has the pitch of 123 Hz. (a) Find the tension of this string. Give the answer in pounds. The density of steel is 7.86 g/cm^3. (b) There are 228 strings in a piano. (Some notes use more than one string.) If we assume that the tension in every string is the same, find the total fouce (in tons, 1 ton=2000 lb) exerted on the frame of the piano. (Add together the tensions of all the strings.) Piano frames are made of steel so that they can withstand this kind of force.

Explanation / Answer

a) we have f=1/T=v/lamda where lamda is the wavelength of the sound = L/2 (L is the length of the string). and v be speed of sound wave. f=v2/L. so v=fL/2 v=sqrt(T/d) where d=D*pir^2. (d is the linear density). so T=v^2*d=(fL/2)^2*D*pir^2 (f : frequency L: length of piano string. D: density r: radius of the string). plug in the value to get Tension.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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