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11) What happens to the average kinetic energy of molecules during the solidhiquid phase change ? 12) a long tube of lenath 50 cm is onor

11) What happens to the average kinetic energy of molecules during the solidhiquid phase change ? 12) a long tube of lenath 50 cm is onor

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### Physics Problems: Kinetic Energy and Harmonics #### Question 11 **What happens to the average kinetic energy of molecules during the solid/liquid phase change?** During the phase change from solid to liquid, the average kinetic energy of the molecules remains constant. #### Question 12 **A long tube of length 50 cm is open on one end and closed on the other end. It is placed in air at room temperature.** a) **What is the frequency of the 5th harmonic?** b) **Draw the tube and a qualitative graph of the excess density at two different times separated by the period / 4 (several answers are possible here).** **Details and Explanation:** - **Tube Specifications**: The tube being considered is 50 cm in length, open at one end, and closed at the other end. This configuration leads to the formation of standing waves where the open end corresponds to an antinode while the closed end aligns with a node. - **Frequency of the 5th Harmonic**: For a tube of length \( L = 50 \) cm (which is 0.5 meters), the frequency of the harmonics can be determined based on the relationship \( f_n = \frac{nv}{4L} \) for odd harmonics (n = 1, 3, 5, ...), where \( v \) is the speed of sound in air (approximately 340 m/s). - **Graph of Excess Density**: The excess density represents the variation from normal air density within the tube due to sound waves. At different times separated by \( \frac{T}{4} \), these variations will illustrate different phases of the standing waves. **Explanation of Diagrams (if applicable):** 1. **Harmonic Representation**: Diagrams could show the position of nodes and antinodes for the 5th harmonic in the tube. 2. **Excess Density Graphs**: Graphs depicting the excess density might show sinusoidal patterns where: - At time \( t = 0 \): A specific distribution of compressions and rarefactions. - At time \( t = \frac{T}{4} \): The distribution shifted by a quarter period of the wave. Understanding these principles is crucial for a comprehensive grasp of harmonics in acoustic physics and the behavior of waves in different media.
Transcribed Image Text:### Physics Problems: Kinetic Energy and Harmonics #### Question 11 **What happens to the average kinetic energy of molecules during the solid/liquid phase change?** During the phase change from solid to liquid, the average kinetic energy of the molecules remains constant. #### Question 12 **A long tube of length 50 cm is open on one end and closed on the other end. It is placed in air at room temperature.** a) **What is the frequency of the 5th harmonic?** b) **Draw the tube and a qualitative graph of the excess density at two different times separated by the period / 4 (several answers are possible here).** **Details and Explanation:** - **Tube Specifications**: The tube being considered is 50 cm in length, open at one end, and closed at the other end. This configuration leads to the formation of standing waves where the open end corresponds to an antinode while the closed end aligns with a node. - **Frequency of the 5th Harmonic**: For a tube of length \( L = 50 \) cm (which is 0.5 meters), the frequency of the harmonics can be determined based on the relationship \( f_n = \frac{nv}{4L} \) for odd harmonics (n = 1, 3, 5, ...), where \( v \) is the speed of sound in air (approximately 340 m/s). - **Graph of Excess Density**: The excess density represents the variation from normal air density within the tube due to sound waves. At different times separated by \( \frac{T}{4} \), these variations will illustrate different phases of the standing waves. **Explanation of Diagrams (if applicable):** 1. **Harmonic Representation**: Diagrams could show the position of nodes and antinodes for the 5th harmonic in the tube. 2. **Excess Density Graphs**: Graphs depicting the excess density might show sinusoidal patterns where: - At time \( t = 0 \): A specific distribution of compressions and rarefactions. - At time \( t = \frac{T}{4} \): The distribution shifted by a quarter period of the wave. Understanding these principles is crucial for a comprehensive grasp of harmonics in acoustic physics and the behavior of waves in different media.
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