The lowest note on a grand piano has a frequency of 28.1 Hz. It is a fixed string oscillating in its fundamental (longest wavelength) mode. The string is 2.00 m long and has a mass of 340 g. What tension is needed to tune this string properly to the frequency of 28.1 Hz

2210.91 N

Explanation:

f = v/∧ = 1/2 √ T/ μ

where f= 28.1 Hz , T= tension ,

L= 2m

mass density =  μ = 350÷1000/2.00

= 0.175kg/m

from  f = 1/2L √ T/ μ

make T the subject of the formula

T= (f×2L)² ₓ  μ

T= (28.1×2×2)² ×0.175

T=12633.76×0.175

=2210.91 N

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle