91Ó°ÊÓ

When discussing sound waves, the wavelength is a crucial concept. It describes the distance between consecutive points of a wave, like crests or troughs. Think of it as the length of one complete wave cycle.
In the original problem, the wavelength of the sound in air is given as 2.74 meters. This is the distance over which the wave pattern repeats. When a sound wave travels from air into water, although its speed changes, the frequency remains the same because it's determined by the source of the sound.
- **Wavelength and Speed:** Upon entering a new medium, the speed of the wave changes but not its frequency. As a result, the wavelength adjusts to match the new speed. This relationship is a fundamental aspect of wave behavior and is expressed by the formula: \[\lambda = \frac{v}{f}\]- **Key Insight:** In the exercise, because the speed of sound in water is higher than in air, the wavelength in water becomes longer. This is because the wave covers more distance in the same amount of time due to the increased speed.

The speed of sound is the rate at which sound waves travel through a medium. It is influenced by the medium's properties, such as density and temperature.
- **Sound in Different Media:** In our problem, the sound wave transitions from air to water. In general, sound travels faster in water than in air primarily because water is denser, allowing sound waves to transmit more efficiently. At 20°C, sound travels at approximately 343 meters per second (m/s) in air and 1482 m/s in water.
Understanding this concept is critical when solving problems involving sound traveling through different media. Given the fixed frequency as the sound moves from air to water, the speed of sound's increased value in water leads to a corresponding change in wavelength to maintain the same frequency. This is crucial for waves maintaining a steady beat despite changing speeds.- **Application of Speed Equation:** The equation relating speed to wavelength and frequency, \( v = f\lambda \), is pivotal here. It helps calculate how the wavelength changes by using known speeds and constant frequency, as demonstrated in the step-by-step solution.

Frequency is a measure of how many wave cycles pass a point in one second and is measured in hertz (Hz). It represents the sound wave's pitch—higher frequencies correspond to higher pitches.
- **Frequency Consistency:** One critical aspect of the problem is that the frequency does not change as the wave moves from air to water. This constancy is because the frequency is set by the source and remains the same regardless of the medium.- **Calculating Frequency:** In the solution, we use the speed of sound in air and the given wavelength to find the frequency. Using the formula: \[ f = \frac{v}{\lambda} \] Substituting in the values gives us the frequency of around 125.18 Hz in both air and water.
- **Importance of Frequency:** The unchanged frequency means that any alterations in speed result in a change in wavelength. This understanding allows us to calculate new wave properties like the wavelength of sound in water, providing a broader appreciation for how sound behaves across different environments.