Find the first two harmonics of a linear mass density .002 kg/m and length 0.60m when it is subjected to tension of 50 N.

To find the first two harmonics of a linear mass density under tension, we need to use the equation for the frequency of a stretched string:

f = (1/2L) * sqrt(T/μ)

Where:
f is the frequency of the string (harmonic),
L is the length of the string,
T is the tension applied to the string, and
μ is the linear mass density of the string.

In this case, we are given:
Linear mass density (μ) = 0.002 kg/m
Length (L) = 0.60 m
Tension (T) = 50 N

Let's calculate the first harmonic (fundamental frequency):

f₁ = (1/2L) * sqrt(T/μ)
= (1/2 * 0.60) * sqrt(50 / 0.002)
= 0.5 * sqrt(25000)
≈ 177.0 Hz

Now, to find the second harmonic, we multiply the fundamental frequency (f₁) by 2:

f₂ = 2 * f₁
= 2 * 177.0 Hz
≈ 354.1 Hz

Therefore, the first harmonic is approximately 177.0 Hz, and the second harmonic is approximately 354.1 Hz.