World-renowned bluegrass musician, Frog Newton, has invited you to join his band

Question

World-renowned bluegrass musician, Frog Newton, has invited you to join his band. It is apparent that he is only looking for eye-candy on the stage, because you are only asked to play one note, the C at a frequency of 261 Hz. You make your own instrument using a string that is 0.6 meters long and has a mass of 2.5 grams. Now you need to calculate the necessary tension on the string, And you will be ready to jam!

What is the wavelength of the first harmonic (also called the fundamental frequency) of standing wave created by the vibrating string
m

At what speed would a wave propagate on this string?
m/s

What is the linear density of the string?
kg/m

What is the tension needed to produce the C note?
N

Explanation / Answer

Mass per length, linera density

mu=2.5/.6 =.417 gram/m=4.12 *10^-4 kg/m

the string has two nodes at the end, and one anti-node in the middle, so therefore the vibrating length of the string (.60 m) is equal to 2/4lambda so lambda = 1.2 m (wavelength)

f=261 hz,

velocity of the wave

v=f*lambda=261*1.2 =313.2 m/s

Tension in the string,

T=mu*v^2=4.12*10^-4*(313.2)^2 =40.41 N.

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