Finding Tension Of A Spring In Waves

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SUMMARY

The discussion centers on calculating the tension of a spring in a sinusoidal wave on a string with a speed of 8.0 cm/s and a linear density of 7.0 g/cm. Initially, the user incorrectly calculated the tension as 448 N by misapplying the formula V = sqrt(Tension/linear density). The correct approach involves using the equation V^2 = T/μ, leading to the accurate tension value of 896 N after squaring the wave speed. This highlights the importance of careful calculation in physics problems.

PREREQUISITES
  • Understanding of wave mechanics and sinusoidal functions
  • Familiarity with the concepts of tension and linear density in strings
  • Knowledge of the formula V = sqrt(T/μ) for wave speed
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation and applications of the wave equation in different media
  • Learn about the effects of linear density on wave speed and tension
  • Explore advanced topics in wave mechanics, such as standing waves and harmonics
  • Practice solving problems involving tension in various physical contexts
USEFUL FOR

Physics students, educators, and anyone interested in understanding wave mechanics and tension calculations in strings.

GingerBread27
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Finding Tension Of A Spring In Waves-Figured Out ALready

A sinusoidal wave is traveling on a string with speed 8.0 cm/s. The displacement of the particles of the string at x = 30 cm is found to vary with time according to the equation y = (5.0 cm) sin[15.0 - (4.0 s^-1)t]. The linear density of the string is 7.0 g/cm.

What is the tension?

Now I just thought V=sqrt(Tension/linear density), meaning you would do 8=sqrt(T/7). This gives Tension=448 N. This answer is wrong. Any ideas?

Never Mind Figured it out! Stupid Mistake
 
Last edited:
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Great job on figuring it out! It's always important to double check your calculations and equations to avoid any mistakes. In this case, it looks like you forgot to square the speed when plugging it into the equation. The correct equation would be V^2 = T/μ, where μ is the linear density. This would give you a tension of 896 N, which is double your previous answer. Keep up the good work!
 

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