Hi there,
I'm trying to understand the propagation of a pulse along a string that is fixed at both ends and am confusing myself. The demonstration I'm using is a long piece of string, tied at one end to the wall and with the other end held by my hand, putting the string under tension. Here's my logic:
1. I jerk the string with my hand, disturbing the string and causing a travelling pulse to travel down the string.
2. I then immediately bring my hand back to the equilibrium position and hold it there. Both ends of the string are now fixed at both ends with the pulse travelling down it.
3. Based on the boundary conditions, the only wave functions which should be allowed on this string are standing waves, but multiple frequencies of standing waves are permitted at once.
4. Therefore, what appears to be a travelling wave pulse is really the superposition of a number of standing waves having different frequencies, phase constants and amplitudes. Although these individual standing waves do not propagate, the net effect of the different frequencies is to give the appearance of a wave that propagates.
Is this logic correct? If not, what am I missing because clearly it is possible to have travelling wave pulses on a string in the situation I've described.
Thanks!
Chris
I'm trying to understand the propagation of a pulse along a string that is fixed at both ends and am confusing myself. The demonstration I'm using is a long piece of string, tied at one end to the wall and with the other end held by my hand, putting the string under tension. Here's my logic:
1. I jerk the string with my hand, disturbing the string and causing a travelling pulse to travel down the string.
2. I then immediately bring my hand back to the equilibrium position and hold it there. Both ends of the string are now fixed at both ends with the pulse travelling down it.
3. Based on the boundary conditions, the only wave functions which should be allowed on this string are standing waves, but multiple frequencies of standing waves are permitted at once.
4. Therefore, what appears to be a travelling wave pulse is really the superposition of a number of standing waves having different frequencies, phase constants and amplitudes. Although these individual standing waves do not propagate, the net effect of the different frequencies is to give the appearance of a wave that propagates.
Is this logic correct? If not, what am I missing because clearly it is possible to have travelling wave pulses on a string in the situation I've described.
Thanks!
Chris
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