SUMMARY
The period of a traveling wave can be calculated using the wave equation y(x,t) = y0 sin(2π(x/λ - t/T)). Given the amplitude of 10.0 cm, wavelength of 8.00 cm, and a displacement of 8.66 cm at x = 15.0 cm and t = 2.00 s, the period is determined to be 1.17 seconds. The approach involves simplifying the equation by setting t to 0, which allows for the cancellation of the period variable, leading to a straightforward calculation. Understanding the relationship between wavelength, amplitude, and period is crucial for solving wave-related problems.
PREREQUISITES
- Understanding of wave equations and trigonometric functions
- Familiarity with concepts of amplitude and wavelength
- Basic knowledge of sine functions and their properties
- Ability to manipulate algebraic equations
NEXT STEPS
- Study the derivation of wave equations in physics
- Learn about the properties of sine and cosine functions
- Explore the relationship between frequency and period in wave mechanics
- Practice solving problems involving wave displacement and phase angles
USEFUL FOR
Students studying physics, particularly those focusing on wave mechanics, as well as educators looking for clear examples of wave period calculations.