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The speed of sound varies significantly based on the medium it travels through because sound is a mechanical wave that requires a material to propagate. In general, sound travels fastest in solids, slower in liquids, and slowest in gases. This is due to the density and elasticity of the medium influencing how quickly particles can transfer the sound energy.

Temperature also affects the speed of sound, as seen with air at different temperatures in the original problem. The speed of sound in air increases with temperature because warmer air has more energy, causing particles to vibrate faster and transmit sound quicker. A formula to estimate the speed of sound in air at different temperatures is:
\[ v_{air} = (331.4 + 0.6 \times T) \text{ m/s} \]
where \( T \) is the temperature in Celsius. Liquids, such as water, have a different relationship with temperature, and an empirical equation is often used to compute the speed of sound in water:
\[ v_{water} = 1402.7 + 4.7 \times T - 0.043 \times T^2 \text{ m/s} \]
Understanding how sound speed changes with mediums and temperatures helps predict how sound waves will behave in various environments.

Snell's Law is a principle that describes how waves, including sound waves, bend when they pass from one medium to another. This bending, known as refraction, occurs due to the change in the wave's speed as it enters the new medium.

For sound, Snell's Law is represented as:\[ \frac{\sin(i)}{\sin(r)} = \frac{v_{medium 1}}{v_{medium 2}} \]
where \( i \) is the angle of incidence, \( r \) is the angle of refraction, and \( v_{medium 1} \) and \( v_{medium 2} \) are the speeds of sound in the two respective mediums. You can use Snell's Law to predict the direction of a sound wave when it crosses into a different medium. As seen in the exercise, the speed of sound in air and water allowed us to calculate how much the sound wave will bend or change direction.

Sound waves are characterized by their frequency, which is the number of waves that pass a point in a given period of time, usually measured in Hertz (Hz). The frequency determines the pitch of a sound—the higher the frequency, the higher the pitch.

One crucial aspect to understand is that the frequency of a sound wave is determined by the source of the wave and remains constant when the wave travels from one medium to another. This constancy was highlighted in the exercise when calculating the frequency of the sound wave in air with:
\[ f = \frac{v}{\lambda} \]
where \( f \) is frequency, \( v \) is the speed of the sound, and \( \lambda \) is the wavelength. Regardless of changes in speed and wavelength when entering a new medium, the frequency stays the same.

The wavelength of a sound wave is the distance between consecutive crests or troughs in the wave. It's inversely related to frequency—sound waves with higher frequencies have shorter wavelengths.

In our exercise, the wavelength changes when the sound wave enters water due to the difference in the speed of sound. The frequency remains constant, but because sound travels faster in water than air, the wavelength increases. We used the speed of sound in water and the constant frequency to find the new wavelength with the formula:\[ \lambda = \frac{v}{f} \]
Hence, the wavelength of the sound wave in water was calculated and showed a significant increase from its original value in air. This concept is essential for understanding how sound behaves differently in various mediums, affecting how we perceive and measure sound.