When a wave travels from one medium to another, like sound waves traveling in the air and then through a glass window pane, it crosses a boundary. Whether the wave continues to the new medium (and even how it goes through), or whether it bounces and reflects back, or a bit of both depends on the boundary.
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Imagine a jump rope attached to a door handle. The last particle of the rope is fixed tot he door handle, and doesn’t move at all. If you grab the free end of the rope and pull it taught, you have a nice, straight line. When you jerk the rope up, the pulse travels through the rope toward the door handle. Some of the energy carried by the pulse is reflected and comes back to you at the same speed and wavelength, but it’s upside down (called a reflected pulse) and not as large amplitude-wise. Some of the energy is also transmitted to the fixed end, causing the door handle to rattle and vibrate.

If you untie the rope from the door handle and instead tie it loosely to a pole (so it’s allowed to slide up and down easily) and repeat this experiment, you’ll find the pulse travels through the rope, turns around and reflects back right side up with the same speed and wavelength.

Now imagine untying the rope and instead attaching a rope denser, thicker rope to the end. The initial pulse travels toward the thicker rope, but two tings happen when it hits the thicker rope: first, a reflected pulse (same speed and wavelength, but inverted) returns back to you, but also some of the energy goes into the thicker rope so a smaller, slower wave (but with the same frequency as the original pulse) will travel along the thicker rope. Waves travel fastest in the least dense medium, so the reflected wave travels faster than the transmitted wave. Even though the waves travel at different speeds in different mediums, they are all vibrating with the same frequency.

What would you expect to happen if a sound wave traveled from the denser rope to a less dense rope? The initial pulse (also called the incident pulse) travels through the denser medium, and when it hits the lesser dense rope, it undergoes partial transmission and partial reflection like this: the reflected pulse  has the same speed and wavelength (and is right side up). Second, the wave transmitted to the less dense rope is right-side up, larger amplitude, and traveling faster than the reflected pulse.

The bottom line? Waves travel fastest in the least dense medium. Frequency doesn’t change when you cross a boundary. The wavelength is always greatest in the least dense rope. The amplitude is always greatest in the initial (incident) wave.

The reflected wave inverts when it moves from a less dense to a more dense rope due to Newton’s Laws of Motion. For the case when the rope is free to slide up and down on the pole, when the initial wave reaches the pole, the rope slides up and because of its inertia, it overshoots and exerts a reaction force on the string, and this reaction force sends a reflected wave back down the string (called a soft reflection). With the case of being fixed on a door handle, when the incident wave reaches the end, it exerts an upward force on the door handle, but Newton’s Third Law states that there’s an equal and opposite (reaction) force that the door handle exerts on the string, which generates an inverted pulse that travels back along the string (called a hard reflection).

Click here to go to next lesson on Wave Reflection.

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