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Let's dive into the fascinating world of travelling waves! A travelling wave is essentially a disturbance that moves through a medium, carrying energy from one place to another without physically transporting the medium itself.
An easy way to recognize a travelling wave is through its mathematical form, often represented as \( y(x, t) = f(vt - x) \) or \( y(x, t) = f(vt + x) \). The term \( vt \) represents the velocity of the wave multiplied by time, denoting its movement through space over time.
In the context of this exercise, we observed that the function \( y(x, t) = f(v+x) \) does not follow the typical pattern of a travelling wave. It lacks the time-dependent term that adjusts with velocity, which is crucial for describing how the wave progresses over time. This illustrates that understanding the mathematical structure of waves helps us predict and describe wave behavior accurately.

When waves encounter a boundary or obstacle, they often undergo reflection. Reflection is when a wave returns into the same medium from which it originated.
When a wave is reflected, several of its properties remain constant, particularly its frequency. This happens because the source of the wave, which dictates frequency, does not change during reflection. However, its wavelength and velocity remain unchanged as well, which aligns with the idea that the wave has not entered a new medium.
It's important to correct a common misconception from the exercise: when waves reflect, their speed and wavelength remain the same while only the direction may change. Understanding these fundamentals of wave reflection is key in fields ranging from acoustics to optics.

Wave refraction is a phenomenon that occurs when waves transition from one medium to another. This shift in medium causes a change in the wave's velocity.
According to Snell's Law, when waves move from a medium of lower speed (like air) to a medium of higher speed (like water), they tend to bend away from the normal line at the interface of the two media.
In the specific case of ultrasonic waves moving from air into water, the speed of sound is higher in water as compared to air. As such, the waves bend away from the normal, contradicting the statement in the exercise which suggested otherwise. Grasping how light and sound waves refract leads to applications in lens designs, audio technology, and more.

The speed of sound varies significantly across different mediums due to differences in molecular structure and density.
Sound waves move faster in solids than in gases like air. This is because molecules in solids are packed closely together, which enables swift transmission of vibrational energy from one molecule to the next.
The exercise introduced this concept by noting that the speed of sound is typically greater in solids than gases at normal temperature and pressure (NTP). This attribute of sound is crucial in fields such as material science, meteorology, and even music production, as it impacts everything from the design of musical instruments to the development of construction materials.