Understanding Period and Frequency in Waves and Pressure Changes

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SUMMARY

The discussion centers on the relationship between angular frequency and wave period in the context of the equation x = cos(π/2 (x - 330t)). The participant initially misunderstands the significance of the coefficient 330, mistaking it for angular frequency (ω). The correct interpretation reveals that 330 represents the wave speed (c), leading to the conclusion that the period T is calculated as T = 330/4, where 4 is derived from the wave's angular frequency. The general wave equation y(t) = cos(ωt + θ) is also referenced, clarifying the definitions of angular frequency and phase angle.

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  • Understanding of wave equations and their general forms
  • Familiarity with angular frequency (ω) and its relationship to frequency (f)
  • Knowledge of wave speed (c) and wavelength (λ)
  • Basic algebra skills to manipulate equations
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  • Study the derivation of wave speed and its relation to frequency and wavelength
  • Learn about angular frequency and its calculation in different wave contexts
  • Explore the concept of phase angles in wave mechanics
  • Practice solving wave equations using various parameters
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Students preparing for physics exams, educators teaching wave mechanics, and anyone seeking to clarify concepts related to wave properties and equations.

Seiya
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Say if i have an equation:

x = cos pi/2 (x-330t)

someone told me that 330/4 is the period. I just want to know how come... what's the 330 represent exactly? i tought it was w (angular frequency) which would mean w/2(pi) = f ... and 1/f = T but i don't get the same results as what he said (330/4) = T...


I'm very confused about this and I've got a test tomorrow... if someone could explain it to me Id very much appreciate it. Thank you
 
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The general form for a wave is

y(t) = cos (\omegat + \theta) where \omega is the angular frequency (= 2\pif) and \theta is the phase angle, which is based on the initial condition. The period T = 1/f, and if the wave speed = c, then c = f\lambda, where \lambda is the wavelength.

Another way to write this expression is

y(x,t) = A sin (\omegat - kx), where k is the wave number, and kx is the phase lag. If kx was preceded by +, the it would represent a phase lead.
 
Oh god how embarassing, all this time i was confused about this topic because of a simple MATH error... i canceled out something i should not have canceled out!

Oh my god *blushes* :(

Thanks for the help... i still can't believe this lol... =\
 
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