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

The first three harmonics of the string are 131.8 Hz, 263.6 Hz and 395.4 Hz.

Velocity of the wave

The velocity of the wave is calculated as follows;

v = √T/μ

where;

• T is tension
• μ is mass per unit length = 2 g/m = 0.002 kg/m

v = √(50/0.002)

v = 158.1 m/s

First harmonic or fundamental frequency of the wave

f₀ = v/λ

where;

• λ is the wavelength = 2L

f₀ = v/2L

f₀ = 158.1/(2 x 0.6)

f₀ = 131.8 Hz

Second harmonic of the wave

f₁ = 2f₀

f₁ = 2(131.8 Hz)

f₁ = 263.6 Hz

Third harmonic of the wave

f₂ = 3f₀

f₂ = 3(131.8 Hz)

f₂ = 395.4 Hz

Thus, the first three harmonics of the string are 131.8 Hz, 263.6 Hz and 395.4 Hz.

Learn more about harmonics here: https://brainly.com/question/4290297

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