Wavelength given time, velocity, and cycles

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SUMMARY

The discussion focuses on calculating the wavelength of longitudinal pulses generated in a spiral spring, given the velocity of the pulse (0.581 cm/s) and the number of cycles completed (2.88 cycles in 6.98 seconds). The correct approach involves converting the velocity to meters per second (0.00581 m/s) and determining the frequency by dividing the number of cycles by the time (0.4126 Hz). The wavelength is then calculated using the formula v = λf, resulting in a wavelength of 0.002397 m, although the initial calculation was flagged as incorrect due to a misunderstanding of the period.

PREREQUISITES
  • Understanding of wave mechanics and properties
  • Familiarity with the relationship between velocity, frequency, and wavelength
  • Basic algebra for manipulating equations
  • Knowledge of unit conversions, specifically between centimeters and meters
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  • Review the principles of wave motion and longitudinal waves
  • Study the derivation and application of the wave equation v = λf
  • Practice unit conversions, particularly between different metric units
  • Explore examples of calculating frequency and wavelength in various contexts
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GiantSheeps
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Homework Statement


As your hand moves back and forth to generate longitudinal pulses in a spiral spring, your hand completes 2.88 back-and-forth cycles every 6.98 s. The velocity of the pulse in the spring is 0.581 cm/s. What is the wavelength? Answer in units of m.

Homework Equations


v=λf
f=1/T

The Attempt at a Solution



First I converted .581 cm/s to .00581 m/s
then I divided 2.88 / 6.98 to get .4126, the period
then I divided 1 / .4126 to get 2.4236, the frequency
and I plugged v and f into the v=λf equation
.00581 / 2.4236 to get .002397 m as the wavelength

but that is incorrect

where did I go wrong? Any help would be greatly appreciated
 
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2.88 cycles in 6.98s = 0.4126 cycles a second is correct.
You state 0.42126 is the period, but does 0.4216 cycles/second really sound like a period to you?

I hope this gets you on the right track cause the rest of your calculations seem valid.
If you still can't get the correct answer let me know!
 
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