Speed of a transverse wave along a wire?

[coffeem]

Homework Statement

A 2kg mass is suspended from a stell wire with a diameter 1mm and a length 0.75m. Caclulate the speed of the transverse wave along the wire.

Homework Equations

v = root(FL/mass)

where F - force of tension, L - length of wire, mass is mass.

The Attempt at a Solution

When I calculate this using the equation in the book I get v = 2.7m/s.

However this fails to take into account the diameter (cross sectional area of the string). Is this correct?

 

[rl.bhat]

In the problem mass of the wire is not given.

density = mass/ volume. = m/πr^2L.

So m/L = ρπr^2 where ρ is the density of the steel wire.

 

[coffeem]

In the problem mass of the wire is not given.

density = mass/ volume. = m/πr^2L.

So m/L = ρπr^2 where ρ is the density of the steel wire.

Are ok. The only problem is that i am not given the density and it has asked me to calculate the velocity of the wave. Given that it is a first year uni question and is only worth one mark, do you think they are expecting me to neglect the mass of the string?

 

[Redbelly98]

No, I very strongly doubt you can neglect the mass of the string.

Perhaps the density of steel and other materials is given somewhere in the chapter that this problem is from. In which case you would be expected to look up the density.

 

[coffeem]

Perhaps the density of steel and other materials is given somewhere in the chapter that this problem is from. In which case you would be expected to look up the density.

Id agree - but this is from a past examination paper... and it is not given? Do you think I am expected to memorize the density of steel? I will email the lecturer to ask, however I have a suspicion that you are meant to take the wire to be massless. I know this is wrong, but will the mass of the wire make a major difference? thanks

 

[Redbelly98]

Homework Equations

v = root(FL/mass)

where F - force of tension, L - length of wire, mass is mass.

"mass" refers to the mass of the steel wire here. It cannot be zero.

The 2 kg mass is only to provide tension in the wire, it does not contribute to "mass" in the above formula.

Best to ask the instructor for clarification at this point. Memorizing the density of anything other than water seems rather pointless to me, but the instructor may have reasons for doing so.

 

[coffeem]

"mass" refers to the mass of the steel wire here. It cannot be zero.

The 2 kg mass is only to provide tension in the wire, it does not contribute to "mass" in the above formula.

Best to ask the instructor for clarification at this point. Memorizing the density of anything other than water seems rather pointless to me, but the instructor may have reasons for doing so.

I see - I have email the lecturer and asked. Ill see what he comes up with... thanks