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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

Intro to Waves

Physics

18. Waves & Sound

Intro to Waves

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3:55 minutes

Problem 71b

Textbook Question

A sinusoidal traveling wave has frequency 880 Hz and speed 440 m/s at a fixed location, by how much does the phase change during a time interval of 1.0 x 10^-4 s?

Verified step by step guidance

Determine the angular frequency (ω) of the wave using the formula: ω = 2πf, where f is the frequency of the wave. Substitute f = 880 Hz into the formula.

Calculate the phase change (Δϕ) using the relationship Δϕ = ωΔt, where Δt is the time interval. Substitute the value of ω from the previous step and Δt = 1.0 × 10⁻⁴ s into the formula.

Simplify the expression for Δϕ by multiplying the angular frequency (ω) with the time interval (Δt).

Express the phase change (Δϕ) in radians, as this is the standard unit for phase in wave mechanics.

Conclude that the phase change during the given time interval is proportional to the product of the angular frequency and the time interval, and ensure the result is in radians.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Wave Frequency

Frequency is the number of cycles of a wave that pass a given point per unit time, measured in hertz (Hz). In this case, the wave has a frequency of 880 Hz, meaning 880 cycles occur every second. This concept is crucial for understanding how quickly the wave oscillates and influences the phase change over time.

Wave Speed

Wave speed is the distance traveled by a wave in a given amount of time, calculated as the product of frequency and wavelength. Here, the wave speed is 440 m/s, indicating how fast the wave propagates through space. This speed is essential for determining how far the wave travels during the specified time interval.

Phase Change

Phase change refers to the difference in the phase of a wave at two different points in time or space, typically measured in radians or degrees. The phase change can be calculated using the formula Δφ = 2πfΔt, where Δt is the time interval. Understanding phase change is key to solving the problem, as it quantifies how much the wave's position shifts over the given time.

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Related Practice

Textbook Question

When you walk with a cup of coffee (diameter 8 cm) at just the right pace of about one step per second, the coffee sloshes higher and higher in your cup until eventually it starts to spill over the top, Fig 15–41. Estimate the speed of the waves in the coffee.

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Textbook Question

A 572-Hz longitudinal wave in air has a speed of 345 m/s. What is the wavelength?

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Textbook Question

A transverse wave pulse travels to the right along a string with a speed v = 2.4 m/s. At t = 0 the shape of the pulse is given by the function D = 4.0m³ / (x² + 2.0m²), where D and x are in meters. Determine a formula for the wave pulse at any time t assuming the pulse is traveling to the left.

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Textbook Question

Show that the displacement D(x,t) = ln(ax + bt), where a and b are constants, is a solution to the wave equation. Then find an expression in terms of a and b for the wave speed.

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Textbook Question

A high-flying jet cruising at 3000 km/h displays a Mach number of 3.1 on a screen. What is the speed of sound at that altitude?

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Textbook Question

A sinusoidal traveling wave has frequency 880 Hz and speed 440 m/s. At a given time, find the distance between two positions that correspond to a difference in phase of π/6 rad.

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Multiple Choice

A satellite captures images of a tsunami, and properties of the tsunami can be found from these images, providing important information to people who need to evacuate coastal areas. If satellite images of a tsunami show the distance from one peak to another is 500 km, and the period is 1 hour, how much time do people have to evacuate if the tsunami is found to be 100 km off shore?

A string with a linear mass density of