Question

A piano string of length 76cm and mass per unit length of 6.91 x 10-3 kg/m is under a tension of value 40N. What is the frequency of a note sounded by this string? (2 mar

Answer 1

Given:

• Length of the piano string =76cm = 0.76 m
•  [pronounced mi] = 6.91 x 10-3 kg/m
• Tension of the value(T)= 40N

To Find

• Frequency(f)of a note sounded by this string.

Formula to be used

• f=[T/$\mu$]^(1/2)/2L

Solution

$\implies$ f = [T / $\mu$ ]^(1/2) / 2L

$\implies$ f = [40 / (6.91 * 10^(-3))]^(1/2) / (2 * 0.76)

$\implies$ f = 50.1 Hz

Note

• f is the frequency in hertz (Hz) or cycles per second

• T is the string tension in gm-cm/s²

• L is the length of the string in cm(later converted into m)

• μ is the linear density or mass per unit length of the string in gm/cm

Typically, tension would be in newtons, length in meters and linear density in kg/m, but those units are inconvenient for calculations with strings. Thus, the smaller units are used.

Hope it helps !