### Correct Option: A. Increase #### Detailed Explanation: When a sound wave travels from a cold air region to a hot air region, its wavelength increases. To understand why this happens, we need to consider the properties of sound waves and how they interact with the medium through which they travel. 1. **Speed of Sound in Different Temperatures**: - The speed of sound in air is affected by the temperature of the air. The general formula for the speed of sound in air is given by: \[ v = 331.3 + 0.6T \] where \( v \) is the speed of sound in meters per second and \( T \) is the temperature in degrees Celsius. As the temperature increases, the speed of sound also increases. 2. **Relationship Between Wavelength, Frequency, and Speed**: - The relationship between the speed of sound (\( v \)), frequency (\( f \)), and wavelength (\( \lambda \)) is given by the equation: \[ v = f \lambda \] - Rearranging this equation gives us: \[ \lambda = \frac{v}{f} \] - This means that the wavelength is directly proportional to the speed of sound when the frequency remains constant. 3. **Transition from Cold to Hot Air**: - When a sound wave moves from a colder region to a hotter region, the speed of sound increases due to the higher temperature. Since the frequency of the sound wave does not change as it moves from one medium to another (it is determined by the source of the sound), the increase in speed results in an increase in wavelength. - Therefore, as the sound wave enters the hot air, the wavelength increases. #### Why Other Options Are Incorrect: - **Option B: Decrease**: - This option suggests that the wavelength decreases when moving to a hotter region. However, as explained, the speed of sound increases in warmer air, leading to an increase in wavelength, not a decrease. - **Option C: Decrease then Increase**: - This option implies a two-step process where the wavelength first decreases and then increases. There is no physical basis for this behavior in the transition from cold to hot air. The wavelength continuously increases as the speed of sound increases. - **Option D: Remain Constant**: - This option suggests that the wavelength does not change at all. However, since the speed of sound changes with temperature, the wavelength must also change if the frequency remains constant. Thus, this option is incorrect. ### Summary of Key Points: - The speed of sound increases with temperature, leading to an increase in wavelength. - The relationship between speed, frequency, and wavelength is given by \( v = f \lambda \). - As sound moves from cold air to hot air, the frequency remains constant while the speed increases, resulting in a longer wavelength. - Understanding the properties of sound waves and their dependence on temperature is crucial for solving related problems. This thorough understanding of sound wave behavior in different temperatures will help you tackle similar questions in your exams effectively!