Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

18. Waves & Sound

Wave Functions

Physics

18. Waves & Sound

Wave Functions

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Multiple Choice

A transverse harmonic wave moving to the left has a wavelength of 2.5 m and a wave speed of 12 m/s. The amplitude of the wave is 0.1 m. At x = 0 and t = 0, the displacement of the wave is y = 0. Write the wave function for this wave.

$y\left(x,t\right)=0.1\sin\left(2.51x+30.2t\right)$

$y\left(x,t\right)=0.1\cos\left(2.51x-30.2t\right)$

$y\left(x,t\right)=0.1\sin\left(2.5x+15.7t\right)$

$y\left(x,t\right)=0.1\sin\left(15.7x+188.5t\right)$

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Verified step by step guidance

Identify the general form of the wave function for a transverse wave moving to the left: y(x, t) = A sin(kx + ωt + φ), where A is the amplitude, k is the wave number, ω is the angular frequency, and φ is the phase constant.

Determine the wave number k using the formula k = 2π/λ, where λ is the wavelength. Substitute λ = 2.5 m into the formula to find k.

Calculate the angular frequency ω using the relationship ω = 2πf, where f is the frequency. First, find the frequency using the wave speed v and wavelength λ with the formula f = v/λ. Substitute v = 12 m/s and λ = 2.5 m to find f, then calculate ω.

Since the wave is moving to the left, the wave function will have a positive sign in front of ωt. The initial condition y(0, 0) = 0 suggests that the phase constant φ is 0 for a sine function.

Substitute the values of A, k, ω, and φ into the wave function y(x, t) = A sin(kx + ωt + φ) to write the complete wave function for the given wave.