About this Video
Discussion of systems with infinite number of degrees of freedom, in particular where the oscillators are identical, harmonic and connected only to their neighbors. Examples include a taut string or a transmission line (two parallel conductors). In this session, we discuss situations where the solution can best be described in terms of traveling or progressive waves or pulses.
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- A massless ring slides on a frictionless rod. The ring is connected to a horizontal taut string. The motion of the ring gives rise to a progressive pulse. The resultant shape of the pulse is calculated. Also calculated are the potential energy and kinetic energy that travel along the string. It is shown that the results are consistent with energy conservation. (0:52:14)
- Two transmission lines, which have different phase velocity and characteristic impedance, are connected. There is a progressive sinusoidal wave on the transmission lines. Reflection and transmission of waves occurs at the junction between the lines. The relation between the frequencies, wavelengths, and amplitudes of the waves on the two lines are calculated. (0:25:09)
A massless ring slides on a frictionless rod. The ring is connected to a horizontal taut string. The motion of the ring gives rise to a progressive pulse. The resultant shape of the pulse is calculated. Also calculated are the potential energy and kinetic energy that travel along the string. It is shown that the results are consistent with energy conservation.
Two transmission lines, which have different phase velocity and characteristic impedance, are connected. There is a progressive sinusoidal wave on the transmission lines. Reflection and transmission of waves occurs at the junction between the lines. The relation between the frequencies, wavelengths, and amplitudes of the waves on the two lines are calculated.