Stuck on some wave problems now. I understand the basica ideas and formulas but these questions seem to be throwing me for a loop.(adsbygoogle = window.adsbygoogle || []).push({});

Question 1:

A massive aluminum sculpture is hung from a steel wire. The fundamental frequency for transverse standing waves on the wire is 200 Hz. The sculpture is then immersed in water so that 1/3 of its volume is submerged. The density of water is 1000 kg/m^3 and the density of aluminum is 2700 kg/m^3

What is the new fundamental frequency?

Since its a standing wave I'm applying lambda = 2*L and f = V/(lambda)

they give us original f which shows:

[tex] 200_{hz} = sqrt(T/\mu)/(\lambda) [/tex]

where [tex] \mu = mass/length [/tex]

so

[tex] 200_{hz} = sqrt(mass * grav/(mass /length))/(2*length) [/tex]

we get length = .03942 meters

Then for the new question we must change Tension to account for the new bouyant force.

I get the new T to be:

T = mass* gravity - density of water * gravity * Volume/3

Soo I get to this point:

[tex] f = sqrt((mass*g-density of water * gravity * Volume/3)/(mass/length))/(2*length) [/tex]

Thats as far as I get, I can't get psat the 3 unknowns. I know I'm missing something as they give me the density of aluminum which I probably need somewhere.

Question 2:

Holding Up under Stress. A string or rope will break apart if it is placed under too much tensile stress. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has density 7830 kg/m^3 and will break if the tensile stress exceeds 7 * 10^8. You want to make a guitar string from a mass of 4.10g of this type of steel. In use, the guitar string must be able to withstand a tension of 900 N without breaking. Your job is the following.

A) Determine the maximum length the string can have

B) Determine the minimum radius the string can have.

C) Determine the highest possible fundamental frequency of standing waves on this string, if the entire length of the string is free to vibrate.

I'm not sure where to start on this one. From what I understand it just wants us to find the the max length that can support a Tension of 900N.

Only equation I can think of with T in it is V = sqrt(T/mu) but V is unknown.

For B I thought I could just use a standar Tensile Stress = F_perp/Area but that doesnt seem to work.

Any suggestions would be much appreciated.

Thanks!

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# Homework Help: Help with wave problems

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