Wave speed, tension, linear density

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SUMMARY

The wave speed on a string is determined by the formula velocity = √(tension/linear density). Given a wave speed of 155 m/s at a tension of 84.0 N, the calculated tension required to achieve a wave speed of 182 m/s is approximately 115.934 N. The linear density used in the calculations was determined to be 0.0035 kg/m. This confirms that tension is expressed in Newtons (N) when calculated directly from the wave speed equation.

PREREQUISITES
  • Understanding of wave mechanics
  • Familiarity with the formula for wave speed on a string
  • Basic knowledge of linear density calculations
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Explore the relationship between tension and wave speed in different mediums
  • Learn about the effects of linear density on wave propagation
  • Investigate the implications of varying tension on string instruments
  • Study advanced wave equations in physics
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Students studying physics, particularly those focusing on wave mechanics, as well as educators and anyone interested in the principles of wave propagation on strings.

sphouxay
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Homework Statement


The wave speed on a string is 155 m/s when the tension is 84.0 N.
What tension will give a speed of 182 m/s?




Homework Equations



velocity= Squareroot(tension/linear density)
linear density = mass/length


The Attempt at a Solution



Well, what I did was assuming that i just plug in the numbers my linear density would be 0.0035, my initial tension of 84 netted 155 m/s, I plugged this same number into find the tension with speed of 182 m/s and my answer was 115.934 after some manipulation of numbers, if this is correct is this answer already in N (Newtons).
 
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As you solve for tension without manipulating the equations the answer is naturally in N.
 

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