A string vibrates in its fundamental mode with a frequency of 200 Hz. The string is 0.64 m long and has a mass of 1.61 g. With what tension must the string be stretched?

Answer 1

v = (T/mu)^0.5
where v is the speed, T is the tension, and mu is the linear density

v = lamda*f ; lambda = 2*L for the fundamental mode, where f is the frequency, and lambda is the wavelength

f = (1/(2*L))*(T/mu)^0.5

1.61 g = 0.00161 kg
mu = 0.00161/0.64

200 = (1/(2*0.64))*(T/mu)^0.5

Plug in mu; use algebra to solve for T