Solving Sine Waves Problem: Find Time for π Radians

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SUMMARY

The sine wave problem discussed involves a wave with a frequency of 10Hz and an amplitude of 5 units, represented by the equation y(t) = A . sin(2.π.f.t + φ). The correct calculation for the time it takes for the phase to reach π radians is 0.005 seconds, while the initial calculation yielded 0.038 seconds. This discrepancy highlights the importance of accurately applying the sine wave formula and understanding phase shifts in wave mechanics.

PREREQUISITES
  • Understanding of sine wave equations and their components
  • Knowledge of frequency and amplitude in wave physics
  • Familiarity with phase shifts in trigonometric functions
  • Basic skills in solving algebraic equations
NEXT STEPS
  • Review the derivation of the sine wave equation y(t) = A . sin(2.π.f.t + φ)
  • Study the concept of phase shifts in trigonometric functions
  • Learn about the relationship between frequency, period, and time in wave mechanics
  • Practice solving similar sine wave problems with varying parameters
USEFUL FOR

Students in physics, engineers working with wave mechanics, and anyone interested in understanding sine wave calculations and their applications.

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A sine wave with a frequency of 10Hz and an amplitude of 5 units phases from zero to 2π radians in a complete cycle. How long does it take for the phase to reach a value of π radians?

y(t) = A . sin (2.π.f.t + φ)

0.1 = 5 x sin (2x∏x10x time + 3.14)

time = 0.038 seconds

But the answer suppose to be 0.005 and I got 0.038.

Thank you!
 
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