Waves in Physics 141: Understanding Sinusoidal Waves and Their Properties - Prof. Wolfgang, Assignments of Physics

Download Waves in Physics 141: Understanding Sinusoidal Waves and Their Properties - Prof. Wolfgang and more Assignments Physics in PDF only on Docsity! 1 Phys141 – Fri 11/17 TODAY: Ch 16, Waves Mon: Read Chapter 17 on sound Wed Review Ch 15-17 HW due MONDAY Example: Sinusoidal Waves For a wave moving at velocity v to the right: Example 16.13 (start) ( )2( , ) siny x t A x vtπ λ ⎡ ⎤= −⎢ ⎥⎣ ⎦ Wave Function, Another Form Wave moves one wavelength λ in one period T: vT = λ or v = λ / T Plug into wave function We can define the angular wave number (or just wave number), k The angular frequency can also be introduced again -> ( , ) sin 2 x ty x t A T π λ ⎡ ⎤⎛ ⎞= −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦ 2k π λ = 2 T πω = ( )( , ) sin ω= −y x t A kx t 2 Generalizing from sinusoidal waves Oscillations: differential equation --> Solution For waves: 22 2 2 2 ω∂ ∂⎛ ⎞= ⎜ ⎟∂ ∂⎝ ⎠ y y t k x ( ) 2 2 2 ( ) cosω ω φ= − ⎯⎯→ = + d x x x t A t dt ( )( , ) sin ω⎯⎯→ = −y x t A kx t? linear wave equation A sinusoidal wave of angular frequency ω Is traveling along a stretched string. The string is brought to rest, and a second traveling wave of angular frequency 2 ω is established on the string. The wave speed of the second wave is Tw ice th at of the fir st. .. Ha lf t ha t o f th e f irs t w av e Th e s am e a s t ha t o f th e.. . Im po ss ibl e t o d ete rm ine 78% 6%3% 14% 1. Twice that of the first wave 2. Half that of the first wave 3. The same as that of the first wave 4. Impossible to determine How to create sinusoidal waves on a String • Each element of the string oscillates vertically with simple harmonic motion – For example, point P