Vibrations of Stretched Strings

v = √(T/m)

n = v/(2l) = (1/(2l))√(T/m)

m = πr²ρ

T = Mg

n ∝ 1/l or nl = constant

n ∝ √T

n ∝ 1/√m

y1 = a sin[(2π/λ)(vt − x)]

y2 = a sin[(2π/λ)(vt + x) + π] = −a sin[(2π/λ)(vt + x)]

y = −2a cos(2πvt/λ) sin(2πx/λ)

λ = 2l/p

n = (p/(2l))√(T/m)

n = (1/(2l))√(T/m)

n = (1/(2l))√(Mg/(πr²ρ))