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To understand diffraction, we first need to calculate the wavelength of the sound. The wavelength determines how the sound waves will spread as they pass through an opening, such as a doorway. Here, frequency and speed of sound are key. Given the speed of the sound is 343 meters per second, and the frequency is 607 Hz, we use the formula: \[ \lambda = \frac{v}{f} \]where \( \lambda \) is the wavelength, \( v \) is the speed of sound, and \( f \) is the frequency.- **Example Calculation:** - Substitute the known values into the formula: \[\lambda = \frac{343}{607} \approx 0.565 \text{ m}\]This calculation shows the sound wavelength to be approximately 0.565 meters. Recognizing that wavelength is the distance between consecutive peaks of a wave is crucial for understanding how sound interacts with openings of different sizes.

Diffraction is a phenomenon that occurs when waves bend around obstacles or through openings. It's particularly noticeable when the size of the opening is comparable to the wavelength of the sound. The diffraction angle gives us an idea of how much the sound wave spreads after passing through an opening.When a single door (0.700 m wide) is open, we can calculate the diffraction angle \( \theta \) using the equation:\[ \sin\theta = \frac{\lambda}{a} \]where \( a \) is the width of the open door. For one door open:- **Substitute the Values:** \[\sin\theta = \frac{0.565}{0.700} \approx 0.807\] - Solve for \( \theta \): \[\theta \approx \arcsin(0.807) \approx 53.62^\circ\]For both doors open (1.400 m wide), using the same formula:- **Substitute the Values:** \[\sin\theta = \frac{0.565}{1.400} \approx 0.404\] - Solve for \( \theta \): \[\theta \approx \arcsin(0.404) \approx 23.84^\circ\]With both doors open, the diffraction angle decreases significantly, indicating less spreading of the sound.

Understanding physics problems, like calculating diffraction, involves grasping the core principles at play. This exercise showcases the application of wave concepts in a real-world scenario.1. **Identifying Known Values:** Begin by identifying the given information and crucial constants, such as the speed of sound and frequency.
2. **Formulating the Problem:** Use basic and relevant equations like the wavelength formula \( \lambda = \frac{v}{f} \) and the diffraction angle formula \( \sin\theta = \frac{\lambda}{a} \).
3. **Substitution and Calculation:** Substitute the known values into formulas systematically, ensuring that units match and calculations are correct.
4. **Interpreting Results:** Analyze the resulting values to understand their physical meaning in the context of the problem, checking if the results are sensible given the scenario.Physics problem solving encourages critical thinking and logical progression from basic principles to specific solutions. Each step in the calculation process should build confidence in applying formulas to similar problems.