What is the length of the string?

In summary: Hey, it was teamwork with @Guneykan Ozgul :smile:I still have more questions to ask. Related to Waves and Sounds, should I do another post?Yes please. A new question would go in its own new thread. :smile:In summary, to calculate the length of a string based on its tension and velocity, the formula is L = (mv^2)/T. The units for mass should be in kilograms or grams, and the units for length should be in meters.
  • #1
ThePhysicsXV
35
0

Homework Statement



A wave along a 15 gram string travels at 756 m/s when it is tightened to 189N?

Homework Equations



V = sqr root T/ m/l

The Attempt at a Solution


[/B]
I got 3.30 x 10^-4
 
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  • #2
ThePhysicsXV said:

Homework Statement



A wave along a 15 gram string travels at 756 m/s when it is tightened to 189N?

Homework Equations



V = sqr root T/ m/l

The Attempt at a Solution


[/B]
I got 3.30 x 10^-4
Welcome to the PF.

That looks kind of small for a length of string... What are the units?

Can you show your work (including units) to solve the equation for the length? :smile:
 
  • #3
Your result seems the mass per unit length not length.
 
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  • #4
Guneykan Ozgul said:
Your result seems the mass per unit length not length.
I'm confuse, so what's the correct formula or way to solving for the length?
 
  • #6
Well, you already knew the formula to calculate the m/L (assuming string is uniform).So you can calculate mass per unit length(m/L) by just puttin v and T into equation. Then you can find L using mass(15 g).
 
  • #7
Guneykan Ozgul said:
Well, you already knew the formula to calculate the m/L (assuming string is uniform).So you can calculate mass per unit length(m/L) by just puttin v and T into equation. Then you can find L using mass(15 g).
So mass is gram or I have to do it on kg
 
  • #8
ThePhysicsXV said:
So mass is gram or I have to do it on kg
You should first convert it to kg to be able to express length in meters. If you use gram you find length in terms of centimeters.
 
  • #9
Guneykan Ozgul said:
You should first convert it to kg to be able to express length in meters. If you use gram you find length in terms of centimeters.
So what's the correct formula?
 
  • #10
ThePhysicsXV said:
So what's the correct formula?
You already wrote it in Post #1.

Just re-arrange it to isolate the length on the lefthand side (LHS) of the equation, and substitute the numbers that you have been given in the problem statement. Be sure to convert to mks units as appropriate.

Please show us your work, and your final solution so that we can check it. :smile:
 
  • #11
I got << Deleted by Mentor >> if no mistake. You should use kg or g depending on your preference to express length.
 
  • #12
Guneykan Ozgul said:
I got L=m/(T/v^2) if no mistake. You should use kg or g depending on your preference to express length.
I got 4.96x10^-6 am I correct?
 
  • #13
Guneykan Ozgul said:
I got << Deleted by Mentor >> if no mistake. You should use kg or g depending on your preference to express length.
Please don't do the student's work for them. That's one of the HH rules. He's almost got it figured out on his own now... :smile:
 
  • #14
ThePhysicsXV said:
I got 4.96x10^-6 am I correct?
Almost certainly not. That length is in meters? Please show your detailed work, including units in your equations.
 
  • #15
berkeman said:
Almost certainly not. That length is in meters? Please show your detailed work, including units in your equations.
L= .015m(189N/756m/s ^2)
 
  • #16
ThePhysicsXV said:
.015m
What's that?
ThePhysicsXV said:
/756m/s ^2
Please use better parenthesis to show what is getting squared and what all the units are...
 
  • #17
ThePhysicsXV said:
I got 4.96x10^-6 am I correct?
I think I see where your error is.

You get that answer if you use the incorrect formula [tex]v = \sqrt{\frac{T}{\frac{L}{m}}}[/tex]

Instead of the correct formula that you listed in Post #1 and is in my Hyperphysics link: [tex]v = \sqrt{\frac{T}{\frac{m}{L}}}[/tex]
 
  • #18
berkeman said:
I think I see where your error is.

You get that answer if you use the incorrect formula [tex]v = \sqrt{\frac{T}{\frac{L}{m}}}[/tex]

Instead of the correct formula that you listed in Post #1 and is in my Hyperphysics link: [tex]v = \sqrt{\frac{T}{\frac{m}{L}}}[/tex]
I got L = (mv^2)/T
 
  • #19
ThePhysicsXV said:
I got L = (mv^2)/T
Good. Now plug in the numbers you were given (and show units in square brackets [] or similar to make sure the units of the final answer are right), and solve! :smile:
 
  • #20
berkeman said:
Good. Now plug in the numbers you were given (and show units in square brackets [] or similar to make sure the units of the final answer are right), and solve! :smile:
L= (.015m*756m/s ^2)/(189)
L= 45.36 m
 
  • #21
ThePhysicsXV said:
L= (.015m*756m/s ^2)/(189)
L= 45.36 m
Bingo! :smile:
 
  • #22
berkeman said:
Bingo! :smile:
You sir is the best! Thanks I still have more questions to ask. Related to Waves and Sounds, should I do another post?
 
  • #23
ThePhysicsXV said:
You sir is the best! Thanks
Hey, it was teamwork with @Guneykan Ozgul :smile:
ThePhysicsXV said:
I still have more questions to ask. Related to Waves and Sounds, should I do another post?
Yes please. A new question would go in its own new thread.
 
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FAQ: What is the length of the string?

What is the definition of length?

Length is a measure of the distance between two points. It is typically measured in units such as meters, centimeters, or feet.

How do you measure the length of a string?

The length of a string can be measured using a ruler or a measuring tape. Simply place one end of the ruler or measuring tape at the starting point of the string and stretch it to the other end to get an accurate measurement.

Is the length of a string constant?

No, the length of a string can vary depending on factors such as tension, temperature, and material elasticity. It can also change if the string is cut or stretched.

Can you measure the length of a string without tools?

Yes, you can use your body as a rough measurement tool. For example, you can use your hand span or the length of your foot to estimate the length of a string.

How does the length of a string affect its properties?

The length of a string can impact properties such as its tension, pitch (in the case of musical strings), and frequency. It can also affect the amount of energy needed to vibrate the string and the amount of time it takes for a wave to travel through the string.

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