Speed of a transverse wave along a wire?

In summary, the student is trying to calculate the speed of a transverse wave along a wire with a mass attached. The problem is that the student is not given the mass of the wire, and is instead supposed to use the equation from a previous chapter. Although the student is able to find the equation using material found in the chapter, they are not given the density of the wire and are asked to calculate the velocity of the wave.
  • #1
coffeem
91
0

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?
 
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  • #2
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.
 
  • #3
rl.bhat said:
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?
 
  • #4
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.
 
  • #5
Redbelly98 said:
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
 
  • #6
coffeem said:

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.
 
  • #7
Redbelly98 said:
"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
 

1. What is a transverse wave?

A transverse wave is a type of wave in which the particles of the medium vibrate perpendicular to the direction of the wave's propagation. This means that the wave moves horizontally or vertically, while the particles move up and down or side to side.

2. How is the speed of a transverse wave along a wire calculated?

The speed of a transverse wave along a wire can be calculated using the formula v = √(T/μ), where v is the speed of the wave, T is the tension in the wire, and μ is the mass per unit length of the wire.

3. What factors affect the speed of a transverse wave along a wire?

The speed of a transverse wave along a wire is affected by the tension in the wire and the mass per unit length of the wire. The type of material the wire is made of and the temperature of the wire can also affect its speed.

4. How does the speed of a transverse wave in a wire compare to the speed of a longitudinal wave?

The speed of a transverse wave in a wire is generally higher than the speed of a longitudinal wave. This is because transverse waves require less energy to propagate and can travel through a medium more quickly.

5. Can the speed of a transverse wave along a wire be changed?

Yes, the speed of a transverse wave along a wire can be changed by altering the tension in the wire or changing the properties of the wire, such as its material or temperature. However, the speed of a transverse wave is also dependent on the medium it is traveling through, so changing the medium can also affect the speed.

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