Question

A piano string having a mass per unit length equal to 4.70 10-3 kg/m is under a tension of 1 400 N. Find the speed with which a wave travels on this string.

Answer 1

Answer:

The speed of the sound wave on the string is 545.78 m/s.

Explanation:

Given;

mass per unit length of the string, μ = 4.7 x 10⁻³ kg/m

tension of the string, T = 1400 N

The speed of the sound wave on the string is given by;

$v = \sqrt{\frac{T}{\mu} }$

where;

v is the speed of the sound wave on the string

Substitute the given values and solve for speed,v,

$v = \sqrt{\frac{T}{\mu} }\\\\v = \sqrt{\frac{1400}{4.7*10^{-3}} }\\\\v = \sqrt{297872.34}\\\\v = 545.78 \ m/s$

Therefore, the speed of the sound wave on the string is 545.78 m/s.