When a transverse wave on a string is reflectred from the free end the phase change produced is-------
When a transverse wave on a string is reflected from the free end, the phase change produced is 180 degrees (or π radians). Here's how you can understand and derive this result:
1. Start by understanding how a transverse wave propagates on a string. In a transverse wave, the particles of the medium (in this case, the string) oscillate perpendicular to the direction of wave propagation.
2. When a wave reaches the free end of a string, it encounters a boundary. At this boundary, the wave can either reflect or transmit.
3. The reflection of a transverse wave at a fixed end (or a free end, which is essentially a fixed end for transverse waves) results in a phase change of 180 degrees.
4. To understand why this phase change occurs, consider the behavior of the particles at the boundary. At the fixed end, the particles of the string cannot move. Therefore, when a wave reaches the fixed end, the particles are forced to come to a halt momentarily before reversing their motion.
5. This reversal of motion at the boundary leads to a 180-degree phase change in the reflected wave compared to the incident wave. In other words, the crests of the incident wave become troughs in the reflected wave, and vice versa.
To sum up, when a transverse wave is reflected from a free end, a phase change of 180 degrees occurs. This can be understood by considering the behavior of the particles at the boundary, where they come to a momentary stop and reverse their motion, resulting in a reversal of the phase of the wave.