Solving Phase Change & Spatial Separation with Wavelength & Velocity

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SUMMARY

The discussion focuses on calculating spatial separation and phase change for a wave with a wavelength of 75 cm and a velocity of 375 m/s. The spatial separation between two points that are 30° out of phase is determined to be 0.0625 m, derived from dividing the wavelength by the number of 30° segments in a full cycle. The phase change over a time interval of 0.5 ms is calculated to be 90°, using the frequency derived from the wave's velocity and wavelength. Both calculations are confirmed as logically sound based on the provided equations.

PREREQUISITES
  • Understanding of wave properties, including wavelength and frequency
  • Familiarity with phase difference and its implications in wave mechanics
  • Knowledge of basic wave equations, specifically u = λ / T
  • Ability to perform calculations involving time intervals and phase changes
NEXT STEPS
  • Study wave mechanics to deepen understanding of spatial separation and phase relationships
  • Learn about the implications of wave velocity on phase changes in different mediums
  • Explore advanced wave equations, including those involving harmonic motion
  • Investigate real-world applications of wave properties in fields such as acoustics and optics
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators seeking to clarify concepts related to phase changes and spatial separation in waves.

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Homework Statement


A wave of wavelength 75 cm has velocity 375 m/s.
a. What is the spatial separation between two points that are 30° out of phase at a particular time?
b. What is the phase change at a particular position for a time change of 0.5 ms?

Homework Equations


u = λ / T



The Attempt at a Solution



a. I did not understand what the term "spatial separation" meant so I tried to use logic to understand it. The way I defined it was the distance (or Δx) between two points with Δδ = 30°. I understood that one cycle of the wave is 0.75 m and 360°. I didn't know whether the velocity changes at any point of the wave trajectory so I assumed it was constant throughout the propegation. So what I did was divide 360 / 30 = 12. I then divided the the wavelength by the 12 30° parts of the wave and got 0.75 / 12 = .0625 m. Not sure if that is the correct answer but unit-wise it made sense to me.

b. I used the formula u = λf and solved for f = u/λ = 500 Hz .
then calculated δ = 360° * f * Δt = 360*500* (5*10^-4) = 90°.
Not sure its right.
 
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Looks good to me!
 

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