3 years ago

A mandolin string's first harmonic is 392 Hz. How long is the string if the wave speed on it is 329 m/s?

1 answer:

Taya2010 [7]3 years ago

6 0

Velocity is given by:
velocity=wavelength×frequency
We note that the wavelength of a wave is twice the length of the string (2w) in the first harmonic.
velocity=329 m/s
wavelength=2w
frequency=392
substituting the values in our equation we get:
329=2w(392)
329=784w
solving for w we get
w=329/784
w= 0.41964~0.42 m

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Aleks [24]

Look at the picture.

Use the Pythagorean theorem.

$(19+r)^2=r^2+35^2\\\\19^2+2\cdot19\cdot r+r^2=r^2+1225\ \ \ |-r^2\\\\361+38r=1225\ \ \ |-361\\\\38r=864\ \ \ |:38\\\\r\approx22.737$

The diameter d = 2r.

Therefore

$d=2\cdot22.737=45.474\approx45.5$

Answer: 45.5