Calculating Mass of a Vibrating String Using Known Quantities

[zengodspeed]

Homework Statement

A second harmonic standing wave has the known quantities of Amplitude (max y at antinode) A, maximum velocity (y=0 at antinode) v, string length L, tension in the string T.

Given that we know that it is second harmonic, we can assume that λ = L

How can one determine the mass of the string?

Homework Equations

The Attempt at a Solution

Attempt at solution:

Using the equation to solve for velocity:

I know that I can find the mass of the object if I can find the wave speed, but without knowing the frequency/period of the wave I do not see how I can find this.

Thanks in advance

 

[Abhishek kumar]

Homework Statement

A second harmonic standing wave has the known quantities of Amplitude (max y at antinode) A, maximum velocity (y=0 at antinode) v, string length L, tension in the string T.

Given that we know that it is second harmonic, we can assume that λ = L

How can one determine the mass of the string?

Homework Equations

View attachment 215526

View attachment 215527

View attachment 215528

The Attempt at a Solution

Attempt at solution:

Using the equation to solve for velocity:

I know that I can find the mass of the object if I can find the wave speed, but without knowing the frequency/period of the wave I do not see how I can find this.

Thanks in advance

You havn't mentioned that either string is fixed at both end or fixed at one end
because normal frequencies of standing wave depend on how end is fixed

 

[zengodspeed]

You havn't mentioned that either string is fixed at both end or fixed at one end
because normal frequencies of standing wave depend on how end is fixed

Hi, sorry about that. The string is fixed at both ends.

 

[haruspex]

the frequency/period of the wave I do not see how I can find this.

Look at your third relevant equation. What does it say about the max v_y?

 

[zengodspeed]

Look at your third relevant equation. What does it say about the max v_y?

That the max v_y is equal to the derivative of the second equation when y=0?

 

[haruspex]

That the max v_y is equal to the derivative of the second equation when y=0?

Just fix on the third equation. As t and x vary, what is the max value of the right hand side?

 

[zengodspeed]

Just fix on the third equation. As t and x vary, what is the max value of the right hand side?

The maximum value of the right hand side would be Aω if x and t were chosen so that sin(kx) and cos(ωt) were both equal to 1.

 

[haruspex]

The maximum value of the right hand side would be Aω if x and t were chosen so that sin(kx) and cos(ωt) were both equal to 1.

Right, so what is the max value of v^y?

 

[zengodspeed]

The max value is equal to Aω. Therefore you can solve for ω by taking the ratio of the v_y,max and the amplitude.

 

[haruspex]

The max value is equal to Aω. Therefore you can solve for ω by taking the ratio of the v_y,max and the amplitude.

Right, and you are given v_y,max.

 

[zengodspeed]

Right, and you are given v_y,max.

Brilliant, thank you very much!