In the Melde's string apparatus, why there is no standing wave in the segment between the pulley and mass hanger?
The energy from the vibrator hits the pulley, and is reflected back, that is in fact the source of standing waves. In the hanging area, no excitation energy enters.
Thanks a lot
In Melde's string apparatus, a standing wave is formed by a continuous string under tension. The segment between the pulley and the mass hanger does not have a standing wave because it is not subjected to any oscillatory motion that creates nodes and antinodes.
To understand this, let's break down the mechanism of a standing wave formation in Melde's apparatus:
1. The apparatus consists of a string that is clamped at both ends and placed under tension using a mass hanger.
2. The string is driven into oscillatory motion by a vibrating source at one end.
3. As the string oscillates, it produces waves that travel along its length.
4. When the length of the string is an integer multiple of half-wavelengths, the waves reflect off the clamped ends and interfere constructively, creating specific points called nodes and antinodes.
- Nodes are points of minimal or no vertical displacement, which always occur at the clamped ends of the string.
- Antinodes are points of maximum vertical displacement and occur at equal intervals between the nodes.
Now, let's consider the segment between the pulley (or drive mechanism) and the mass hanger:
- This segment of the string is not directly involved in the oscillatory motion. It is merely serving as a connecting element between the drive mechanism and the mass hanger.
- Therefore, there are no waves being generated in this particular segment.
- Without waves, there is no oscillation to create nodes and antinodes, and thus no standing wave is formed in this segment.
In summary, the absence of a standing wave in the segment between the pulley and the mass hanger in Melde's string apparatus is due to the fact that this segment is not actively involved in the oscillatory motion that generates the standing wave.