Why is sqrt(Tension/(mass/lenght)) = f*lambda - Standing Waves

[Bastian]

Homework Statement

So in our report we have to explain why these formulas give the same answer theoretically.
We have for an example measured these numbers:

Freq.: 16,37 Hz
L: 1m
m: 0.007 kg
T ≈ 1 N
λ=1/1=1

Homework Equations

v=ƒ*λ=√T/(m/L)

The Attempt at a Solution

The problem is that I don't get why some constants in √T/(m/L) would give you the same answer as: ƒ*λ, because you don't have the freq. nor the wavelength in √T/(m/L)

If any further questions need to be asked feel free - I would really like to understand this :)

 

[haruspex]

Homework Statement

So in our report we have to explain why these formulas give the same answer theoretically.
We have for an example measured these numbers:

Freq.: 16,37 Hz
L: 1m
m: 0.007 kg
T ≈ 1 N
λ=1/1=1

Homework Equations

v=ƒ*λ=√T/(m/L)

The Attempt at a Solution

The problem is that I don't get why some constants in √T/(m/L) would give you the same answer as: ƒ*λ, because you don't have the freq. nor the wavelength in √T/(m/L)

If any further questions need to be asked feel free - I would really like to understand this :)

Equations mean nothing without context. Please specify the physical set-up. (You should normally specify what each variable means in the context, but it should be clear in this case.)
I did not understand the reference to constants. Did you mean variables?
There are two levels of explanation that may be available, depending on what exactly you are being asked. At one level, it might be easy to show that the two formulae lead to the same, up to a possible constant ratio. Dimensional analysis is often capable of that. To show that they are exactly the same, i.e. a ratio of 1:1, will take a more detailed analysis of the physical system.

 

[Bastian]

All right, so:
This was our setup:
https://www.dropbox.com/s/00piqo83iv5tbve/Billede 11-10-2016 13.27.36.jpg?dl=0

We had an oscillator at one end, and then the string kept at 1 meter all the time. That's why I wrote constant. Because the length of the string is constant the mass of the string is also constant.
Over the tip off the table there were some strings with some weight .1kg of mass hanging in it to create tension.

So what I'm wondering is why the formula including tension, mass and length can give me the speed of the string. For all it matters the string could be doing nothing.

I know why the numeric values is equal to each other (as the frequency goes up the lambda values go down. Equaling the same speed). But why can, in my case, some constants equal a speed regardless of what the frequency or wavelength is?
Makes sense? I hope so. And excuse me for my bad English...

 

[haruspex]

why can, in my case, some constants equal a speed regardless of what the frequency or wavelength is?

I will reword that as "why can some parameters determine the speed, independently of frequency and wavelength?"
If we suppose the speed is a function of mass per unit length, ρ, tension, T, and frequency, f, and wavelength, λ, then we can use dimensional analysis to show that specifically it depends on the combinations √(T/ρ) and fλ.
If we use our general knowledge of waves, we can say that the velocity must equal fλ.
We know that the wavelength is constrained by the length of the string, so we can take v=fλ as determining f from v and λ. It folows that v is a property of the T and ρ combination.
This gets us as far as saying v=fλ=k√(T/ρ) for some constant k. To find k we need to examine the forces and accelerations in detail.

 

[Bastian]

I don't know that truly answers my question:
'cause what I'm really wondering is why (im my case) the constants (T,L,m) can describe the speed of the wave... For all I could think the speed could be 0 aka the "standing wave" would just be a laying string. Makes sense?

 

[haruspex]

I don't know that truly answers my question:
'cause what I'm really wondering is why (im my case) the constants (T,L,m) can describe the speed of the wave... For all I could think the speed could be 0 aka the "standing wave" would just be a laying string. Makes sense?

A standing wave occurs when two equal waves travel in opposite directions. In terms of theory, you should think of the speed of each of those superimposed waves.