Physic I Lab: resonance frequency?

Question

1. Do the resonance frequencies depend on the tension of the string?
2. Do the resonance frequencies depend on on the mass density of the string?
3. Do the resonance frequencies depended on the length of the string?
4. Two strings equal in length and made of the same material are sujected to tensions in the proportion of 1:4; the one under the greater tension is the thicker string. If they vibrate at the same frequency, how do their diameters compare?

Answer 1

freq string under tension (f) = (1/k*L)√(T/m)
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k is constant depending as to how it vibrates, plucked etc
k =2 for fundamental freq
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m = mass/length = linear mass density
T = tension (N), L = length
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1) yes, 2) yes, 3) yes[for 2 wires, 1m and 2m density is same but greater L will allow lower freq.
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m = mass/L = pi(D/2)^2 L / L = pi(D/2)^2 = 0.25 pi D^2
4) (f1) = (1/k*L)√T/(0.25pi D-thin^2)
(f2) = (1/k*L)√4T/(0.25pi D-thick^2)
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f2/f1 = √(4T/(0.25pi D-thick^2) √(0.25pi D-thin^2)/T
f2/f1 = √(4D-thin^2 /(D-thick^2)
2 [D-thin /D-thick] = f2/ f1 = 1
given f1 =f2
D-thick = 2 D-thin

Answer 2

Answers 1-3 are all yes. What is the formula in the book for resonance frequencies?

Answer 3

i'm uncertain of the right formulation, yet as straight away as you strike the tuning fork, position it over the glass tube and carry and shrink the tube untill the pitch of the noise is at this is loudest. you'll want to appreciate the right temperature of the room and in case you'll discover the formulation, enter the area from the right of the tube to the water and some how calculate interior the room temp. The formulation will degree the wave length of the sound waves and furnish you a frequency. With a topic-loose volume of trig you'll want to be waiting to determine it out. Sorry i do not realize the formulation.