A typical steel piano string has diameter of 0.7 mm, which works out to a mass p

Question

A typical steel piano string has diameter of 0.7 mm, which works out to a mass per unit length of about mu=0.003 kg/meter. Calculate the approximate wavespeed in the wire from the formula: v= Squareroot t/mu assuming the tension is T=700 Newtons. Your answer will have units of meters/sec. For C_8, with a frequency of f=4186 Hertz, the wavelength would be ?lambda=v/f. The "speaking length" of the string would be half the wavelength. Calculate the length of the string (your answer will be in meters). Compare to the value we measured in class of about 5 cm. Calculate the length fo C_4. Compare to the value measured in class of about 54 cm If the bass strings were made of the same wire, with the same tension, how long would the C_1 string need to be?

Explanation / Answer

a) formula given
v = 483.05 m/s

b) wavelength = 0.115m
   length = 0.0577 m = 5.77cm > 5cm
c) for C4 frequency is = 261.6 Hz
wavelength = 1.85 m
   length = 1.85/4 m = 0.4625 m = 46.25cm<54cm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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