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phys124s11-hw06 - HW 6 Solutions Wave Notation a Traveling...

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1 HW 6 Solutions Wave Notation a) Traveling waves propagate with a fixed speed usually denoted as v (but sometimes c ). The velocity v is the phase velocity. The waves are called periodic if their waveform repeats every time interval T . The fundamental relationship among frequency, wavelength, and velocity is v f λ = . This relationship may be visualized as follows: In 1 s, ( ) 1 f s cycles of the wave move past an observer. In this same second the wavetrain moves a distance ( ) 1 v s . b) Solve this equation to find an expression for the wavelength λ . / v f λ = c) If the velocity of the wave remains constant, then as the frequency of the wave is increased, the wavelength decreases . d) The difference between the frequency f and the frequency ω is that f is measured in cycles per second or hertz (abbreviated Hz) whereas the units for ω are radians per second. e) Find an expression for the period of a wave T in terms of other kinematic variables. Express your answer in terms of any of f , v , ω , and simple constants such as π . 1 2 T f v π λ ω = = = f) What is the relationship between ω and f ? 2 f ω π = g) What is the simplest relationship between the angular wavenumber k and just one of the other kinematic variables? Express your answer using only one of the other kinematic variables plus constants like π . 2 k π λ = Vibrating String An oscillator creates periodic waves on a stretched string. a) If the period of the oscillator doubles, what happens to the wavelength and wave speed? T v λ = - the phase velocity remains unchanged (it’s a property of the medium in which the wave propagates), λ also doubles.
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