phys124s11-hw06

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 vf 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 vs . b) Solve this equation to find an expression for the wavelength 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 . 12 T f v π ω = == f) What is the relationship between ω and f ? 2 f = 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 = 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 = - the phase velocity remains unchanged (it’s a property of the medium in which the wave propagates), λ also doubles.
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b) If the Both wav speed rem varied on the wave Test You the w point the w point the w the w point the w point none not e A one-di determin that are waveleng apart osc The poin Q are ½ c e amplitude velength and mains uncha nly by chang es. ur Understa wave has the ts are 1/4 cy wave has the ts are in pha wave has a d wave has the ts are 1/2 cy wave has the ts are 1/8 cy e of the abov enough infor imensional s ne the phase 1, 2, 3, . .. gths apart os cillate ¼ cycl nts P and Q a cycle out of of the oscill d wave spee anged, unless ging the freq anding 15.2: same ampli ycle out of ph same ampli ase ifferent amp same ampli ycle out of ph same ampli ycle out of ph ve rmation is gi sinusoidal w relationship . wavelengt scillate ½ cy le out of pha are 0.375 m a phase. lator doubles ed are uncha s the propert quency, or a : Periodic W itude at poin hase itude at poin plitude at poi itude at poin hase itude at poin hase ven to decid wave has the between th hs apart os cle out of ph ase. In this si apart, which 2 s, what happ anged. Whe ties of the str alternatively Waves Cons tube sinus 8 × 10 wave statem nt P as at poin nt P as at poin int P than at nt P as at poin nt P as at poin de e same amp e oscillation scillate in p hase; and po ituation the w h is 1.50 wav pens to the w en waves tra ring are chan the period, sider two po as shown. T soidal longi 0 2 Hz is pro e speed in th ment is corre nt Q, but the nt Q, and the point Q nt Q, but the nt Q, but the
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This note was uploaded on 09/15/2011 for the course APHY 124 taught by Professor Eins during the Spring '11 term at SUNY Albany.

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

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