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1. Intro to Physics Units1h 29m
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5. Projectile Motion3h 6m
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15. Rotational Equilibrium3h 39m
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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
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24. Electric Force & Field; Gauss' Law3h 42m
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26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
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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

Phase Constant

Physics

18. Waves & Sound

Phase Constant

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3:01 minutes

Problem 29c

Textbook Question

A 572-Hz longitudinal wave in air has a speed of 345 m/s. At a particular instant, what is the phase difference (in degrees) between two points 4.4 cm apart?

Verified step by step guidance

Determine the wavelength of the wave using the formula:

λ = \frac{v}{f}

, where

v

is the speed of the wave (345 m/s) and

f

is the frequency (572 Hz).

Convert the distance between the two points (4.4 cm) into meters by dividing by 100, since 1 cm = 0.01 m.

Calculate the fraction of the wavelength that corresponds to the distance between the two points using the formula:

fraction = \frac{d}{λ}

, where

d

is the distance (in meters) and

λ

is the wavelength.

Convert the fraction of the wavelength into a phase difference in degrees using the formula:

phase = \frac{fraction \times 360}{1}

, since one full wavelength corresponds to 360 degrees.

Express the phase difference as the final result, ensuring it is within the range of 0 to 360 degrees (if necessary, subtract multiples of 360 to bring it into this range).

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Key Concepts

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

Wave Speed

Wave speed is the distance a wave travels per unit of time. In this case, the speed of the longitudinal wave in air is given as 345 m/s. This speed is crucial for determining how quickly the wave propagates through the medium and is essential for calculating the phase difference between two points.

Wavelength

Wavelength is the distance between successive points of similar phase in a wave, such as crest to crest or trough to trough. It can be calculated using the formula λ = v/f, where v is the wave speed and f is the frequency. For the given wave, the wavelength can be determined, which is necessary for finding the phase difference over a specified distance.

Phase Difference

Phase difference refers to the difference in the phase of two points in a wave, typically measured in degrees or radians. It indicates how far one point is ahead or behind another in the wave cycle. The phase difference can be calculated using the formula Δφ = (2π/λ) * Δx, where Δx is the distance between the two points, allowing us to find the phase difference for the specified distance of 4.4 cm.

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Related Practice

Textbook Question

A 572-Hz longitudinal wave in air has a speed of 345 m/s. How much time is required for the phase to change by 90° at a given point in space?

Multiple Choice

A wave traveling to the right has an Amplitude of 15 cm, wavelength of 40 cm, and oscillates 8 times per second. At t = 0, the displacement of a particle at x = 0 along this wave is +15 cm. Write the wave function, including the phase constant, using a sine function.

FIGURE P16.45 is a snapshot graph at t = 0 s of a 5.0 Hz wave traveling to the left. Write the displacement equation for this wave.

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Textbook Question

A wave on a string is described by $D (x, t) = (2.00 cm) \times \sin [(12.57 rad/m) x - (638 rad/s) t]$ , where $x$ is in $m$ and $t$ in $s$ . The linear density of the string is $5.00 g slash m$ . What are The maximum speed of a point on the string?

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Textbook Question

A 572-Hz longitudinal wave in air has a speed of 345 m/s. How much time is required for the phase to change by 90° at a given point in space?

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