MHB Sounds waves and guitar strings

[Mango12]

C=130Hz
G=196Hz
D=293Hz
A=440 Hz

The distance from the nut to the bridge is 58cm, the amplitude of the string vibration is 2.2mm

Part A: What is the period (T) of the G string?
Part B: What is the side to side velocity of the g string? (Think simple harmonic motion)
Part C: The diameter of the A string is 0.229mm. What is the diameter of the D string if the tension of both string must be equal?

I don't really know how to approach this, and any help would be appreciated. Thank you.

 

[Mango12]

C=130Hz
G=196Hz
D=293Hz
A=440 Hz

The distance from the nut to the bridge is 58cm, the amplitude of the string vibration is 2.2mm

Part A: What is the period (T) of the G string?
Part B: What is the side to side velocity of the g string? (Think simple harmonic motion)
Part C: The diameter of the A string is 0.229mm. What is the diameter of the D string if the tension of both string must be equal?

I don't really know how to approach this, and any help would be appreciated. Thank you.

UPDATE: I figured out how to do part A, but I still need help with part B and C

 

[I like Serena]

C=130Hz
G=196Hz
D=293Hz
A=440 Hz

The distance from the nut to the bridge is 58cm, the amplitude of the string vibration is 2.2mm

Part A: What is the period (T) of the G string?
Part B: What is the side to side velocity of the g string? (Think simple harmonic motion)
Part C: The diameter of the A string is 0.229mm. What is the diameter of the D string if the tension of both string must be equal?

I don't really know how to approach this, and any help would be appreciated. Thank you.

Hi Mango12! ;)

B. The length of the string corresponds to half of the wave length, which is how it vibrates.
C. Do you have a formula that includes the diameter of the string?

 

[Mango12]

Hi Mango12! ;)

B. The length of the string corresponds to half of the wave length, which is how it vibrates.
C. Do you have a formula that includes the diameter of the string?

I figured out part B, but now I just have to do C.

I don't have any formulas with diameter in them. The only formula I have relating to tension is f=1/2\sqrt{tension/ML}

 

[I like Serena]

I figured out part B, but now I just have to do C.

I don't have any formulas with diameter in them. The only formula I have relating to tension is f=1/2\sqrt{tension/ML}

What is ML?

 

[Mango12]

M is mass and L is length of the string...unless you know a different formula? And I also have V=\sqrt{tension/(m/L)}

 

[I like Serena]

M is mass and L is length of the string...unless you know a different formula? And I also have V=\sqrt{tension/(m/L)}

Isn't the mass dependent on the diameter? (Wondering)

 

[Mango12]

Isn't the mass dependent on the diameter? (Wondering)

I'm not sure, what to do with this, but I just need Part C: The diameter of the A string is 0.229mm. What is the diameter of the D string if the tension of both string must be equal? I feel like tension cancels out somewhere?