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

Tension, T = 2038.09 N

Step-by-step 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=(1)/(2L)\sqrt{(T)/(\mu)}`

`\mu=(m)/(l)`

`\mu=(0.44)/(2)=0.22\ kg/m`

`T=4L^2f\mu`

`T=4* (1.75)^2* (27.5)^2 * 0.22`

T = 2038.09 N

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