Question

The lowest note on a grand piano has a frequency of 27.5 Hz. The entire string is 2.00 m long and has a mass of 440g . The vibrating section of the string is 1.75m long.What tension is needed to tune this string properly?

Answer 1

Answer:

Tension, T = 2038.09 N

Explanation:

Given that,

Frequency of the lowest note on a grand piano, f = 27.5 Hz

Length of the string, l = 2 m

Mass of the string, m = 440 g = 0.44 kg

Length of the vibrating section of the string is, L = 1.75 m

The frequency of the vibrating string in terms of tension is given by :

$f=\dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}$

$\mu=\dfrac{m}{l}$

$\mu=\dfrac{0.44}{2}=0.22\ kg/m$

$T=4L^2f\mu$

$T=4\times (1.75)^2\times (27.5)^2 \times 0.22$

T = 2038.09 N

So, the tension in the string is 2038.09 N. Hence, this is the required solution.