Velocity of Wave in Twice the Radius String: V = root(Tension/mu) * root2

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SUMMARY

The speed of a wave traveling along a string is determined by the formula V = √(Tension/μ), where μ represents the mass per unit length. When the radius of the string is doubled while maintaining the same material and tension, the mass per unit length (μ) also doubles due to the increased cross-sectional area. Consequently, the new wave speed becomes V' = V/√2, resulting in a wave speed of 280 m/s divided by √2, which is approximately 198 m/s. This manipulation confirms that doubling the radius decreases the wave speed due to the increase in mass per unit length.

PREREQUISITES
  • Understanding of wave mechanics and wave speed equations
  • Familiarity with the concepts of tension and mass per unit length (μ)
  • Basic knowledge of geometry related to cross-sectional area
  • Experience with algebraic manipulation of formulas
NEXT STEPS
  • Study the relationship between tension and wave speed in different materials
  • Explore the effects of varying cross-sectional areas on wave propagation
  • Learn about the implications of uniform density in wave mechanics
  • Investigate the impact of string length on wave speed
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Physics students, engineers, and anyone interested in understanding wave dynamics in strings and materials.

lostie100
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A wave travels along a string at a speed of 280m/s. What will the speed if the string is replaced by one made of the same material and under the same tension but having twice the radius?

V = root (Tension/mu)

mu = mass/length

length is 2radii

I manipulated the formulas, however, apparently you divide the velocity by 2, but I found it to be multiplied by root2.
Please show me the manipulation of the formulas...
 
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Assuming uniform density what happens when you double the cross-section of the string that remains the same length? Does the total mass of the string change? By how much?

Plug in your numbers then and see what happens.
 
The mass also doubles...but I don't see how it relates to the other formula for velocity...
 

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