Standing Waves Problem with Unknown Mass

[NP04]

Homework Statement

See Image. Parts C and D

Relevant Equations

Part C.
v = λf
Harmonic numbers for springs

Part D.
x = Acos(ωt). ??? Not really sure what formula to use.

Part C.

First of all, I am not entirely sure what the problem means by "loops." (I see the loops, duh ;)) but I am not sure what quantity they represent. I am guessing it means harmonics, in which case M would have to be lessened to make a greater wavelength. This is because the extension of the string would be lessened as it is less taut. In the relation L = 1/2λ+nλ/2 (4th harmonic for strings), we see that the dividend is

Is this the correct way of thinking about this part?

Part D.

x = Acos(ωt) = Acos(2πf)
4 = Acos((2π)((2π/3)) converted 120 degrees to radians
4 = A(1)
A = 4
The solution says it is 1. I can't think of any alternative to solve this.

Thanks in advance.

 

[haruspex]

not sure what quantity they represent.

What is the relationship between the length of each loop and the wavelength?

the extension of the string would be lessened as it is less taut

That is not a useful way to look at it. You should be able to quote a formula relating tension, density and wave velocity.