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Calculating mass per unit length of a wire

I have the following question in my physics book:

The tension of a wire in Q1 was 40N. Calculate (a) the mass per unit length of the wire, (b) the diameter of the wire if it's density is (mass per unit volume) was 7800kg^-3

Question 1 says: A strenched wire of 0.80m vibrates at its first frequency of 265 Hz. Calculate (a) the wavelenth of the progressive waves on the wire, (b) the speed of the progressive waves of the wire.

I don't know how to do this. I've looked on the internet and found this formula:
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/E2120D0201.gif

I tried using it and ended up with the answer 4194.304 so that can't be it.
I also looked through my book and I can't find anything that helps. This question https://www.thestudentroom.co.uk/showthread.php?t=3790141 answers part (b) but I need help with part (a)
Original post by Simon33355
I have the following question in my physics book:

The tension of a wire in Q1 was 40N. Calculate (a) the mass per unit length of the wire, (b) the diameter of the wire if it's density is (mass per unit volume) was 7800kg^-3

Question 1 says: A strenched wire of 0.80m vibrates at its first frequency of 265 Hz. Calculate (a) the wavelenth of the progressive waves on the wire, (b) the speed of the progressive waves of the wire.

I don't know how to do this. I've looked on the internet and found this formula:
http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/E2120D0201.gif

I tried using it and ended up with the answer 4194.304 so that can't be it.
I also looked through my book and I can't find anything that helps. This question https://www.thestudentroom.co.uk/showthread.php?t=3790141 answers part (b) but I need help with part (a)

I think you need to rearrange the fundamental frequency equation, f=1/2l √(T/μ). You can rearrange that to get μ = T/(2Fl)^2. Then you can sub in the values from the question, so μ = 40/(2*265*0.8)^2, giving a mass per unit length of 2.22 x 10^-4 kgm^-1.

I've attached a screenshot of what I did which shows it a bit more clearly. If you had the mass of the 0.8m of wire given in the question, you could just use μ = m/l, but since that's not given I think this is the way to do it.

I've never seen a question like that before so I'm not sure if it's the right method to do it but the final answer makes sense as strings generally are not heavy, but you may want to check it out if you have the answers.

Hope this helps.
Mass per Unit Length Question.PNG9.7KB
Reply 2
Avatar for sym4
sym4
Bro the frequency is 256 I think

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