waves_03 - 1 waves_03 TRANSVERSE WAVES ON STRINGS...

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waves_03 TRANSVERSE WAVES ON STRINGS 1 Animations courtesy of Dr. Dan Russell, Kettering University

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Travelling transverse waves, speed of propagation, wave function, string tension, linear density, reflection (fixed and free ends), interference, boundary conditions, standing waves, stationary waves, SHM, string musical instruments, amplitude, nodes, antinodes, period, frequency, wavelength, propagation constant (wave number), angular frequency, normal modes of vibrations, natural frequencies of vibration, fundamental, harmonics, overtones, harmonic series, frequency spectrum, radian, phase, sinusoidal functions aves_03: MINDMAP SUMMARY - TRANSVERSE WAVES ON STRINGS v = F T μ s s m L μ= 2 2 1 2 2 v f f T k T k T f λ ϖ π = = = = = = =
3 The string (linear density μ ) must be under tension F T for wave to propagate • increases with increasing tension F T decreases with increasing mass per unit length independent of amplitude or frequency v = F T s s m L μ= TRANSVERSE WAVES ON STRINGS Wave speed v (speed of propagation) linear density

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4 Problem 1 use the ISEE method
5 Solution 1 F = 25.0 N μ = 2.50 g.m -1 = 2.50×10 -3 kg.m -1 f = 50.0 Hz A = 5.00 mm = 5×10 -3 m v = ? m.s -1 ϖ = ? rad.s -1 T = ? s λ = ? m T v = Speed of a transverse wave on a string speed of a wave v f = ( 29 ( 29 -1 -1 3 -1 2 -1 2 25 m.s 100 m.s 2.5 10 2 2 50 rad.s 3.14 10 rad.s 1 1 s 2.00 10 s 50 100 m 2.00 m 50 T v f T f v v f f π - - = = = × = = = × = = = × = = = =

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6 Pulse on a rope When pulse reaches the attachment point at the wall the pulse is reflected If attachment is fixed the pulse inverts on reflection If attachment point can slide freely of a rod, the pulse reflects without inversion If wave encounters a discontinuity, there will be some reflection and some transmission Example: two joined strings, different μ . What changes across the discontinuity - frequency, wavelength, wave speed ?
Reflection of waves at a fixed end Reflected wave is inverted π / 2 PHASE CHANGE Reflection of waves at a free end Reflected wave is not inverted ZERO PHASE CHANGE 7

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waves_03 - 1 waves_03 TRANSVERSE WAVES ON STRINGS...

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