Please Show All Intermediat Steps with Equations and Explina

Please Show All Intermediat Steps with Equations and Explinations, so i can follow allong. I am struggaling with this chapter and need good explination.

Solution

m/L = 6.3 * 10^-4 kg/m

f = 230 hz, l = 1.50 m

a) lambda = 2 L

lambda * f = sqrt [F_T / (m/L)]

3 * 230 = sqrt [F_T / 6.3 * 10^-4 ]

F_T = 230² * 3² * 6.3 * 10^-4

F_T = 299.9

mass = = 299.9 / 9.8

mass = 31 kg

--------------------------------------------------

b) lambda = L

lambda * f = sqrt [F_T / (m/L)]

1.5 * 230 = sqrt [F_T / 6.3 * 10^-4 ]

F_T = 230² * 1.5² * 6.3 * 10^-4

F_T = 74.98

mass = 74.99 / 9.8

mass = 7.65 kg

----------------------------------------------------

lambda = 2.5 * L

0.6 * 230 = sqrt [F_T / 6.3 * 10^-4 ]

F_T = 11.99

mass = 11.99 / 9.8

m₅ = 1.22 kg