Question

Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when the tension in it is 50.0 n.

Answer 1

As we know that Nth harmonic of the string is given by

$f = \frac{N}{2L}\sqrt{\frac{T}{m/L}}$

now here we will have

$m/L = mass density = 2 g/m$

$m/L = 0.002 kg/m$

$Length = L = 0.600 m$

$Tension = T = 50.0 N$

now from above formula we have

$f = \frac{N}{2(0.600)}\sqrt{\frac{50.0}{0.002}}$

$f = 131.8N$

now for first harmonic N = 1

$f_1 = 131.8 Hz$

for second harmonic N = 2

$f_2 = 263.5 Hz$

for third harmonic N = 3

$f_3 = 395.3 Hz$