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16_Waves - INDIANA UNIVERSITY DEPARTMENT OF PHYSICS P309...

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INDIANA UNIVERSITY, DEPARTMENT OF PHYSICS, P309 LABORATORY Laboratory #16: Dispersion of Surface Waves Goal: Investigate how the propagation velocity of surface waves depends on the wavelength Equipment: Ripple tank, linear motion device (Central Scientific #36803), function generator (Global Specialties 2002), audio amplifier, frequency counter (Fluke 1900A), surface tension torsion balance (White type E2), small-weight set (Ohaus), inch tape. Mounted at the ceiling: triggerable stroboscopic light source (Pasco SF9211), iris diaphragm for stroboscope. (A) Physics: In general, a wave is described by a periodic function of position and time. For one- dimensional waves, u , (1) ) ( 0 ) , ( t kx i e u t x ω ± = where k is the wave number and ω the angular frequency which can also be expressed in terms of the wavelength ( k =2 π / λ ) or the frequency f ( ω =2 π f ). The propagation velocity of the wave is v= λ f . A medium is called dispersive when v is not a constant, but depends on λ (or, k). An example of dispersive wave propagation is a wave on the surface of a layer of liquid. The depth of the liquid shall be h . One can then derive an expression for v( λ ) (see refs. [KAU63], [LAM45]): ) tanh( ) ( h k k k g k
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