TSN-3 Two speakers 4.00m apart sit against the middle of one wall of a room that measures 10.0m by 30.0m. They produce sound with a wavelength of 0.900m a) What is the difference in path length for the waves from the two speakers that arrive at point C in the corner of the room as shown to the right? b) Trung stands against the right-hand wall at point O directly in front of the two speakers. If Trung starts walking toward corner C, how many maxima will he hear after leaving point O before he reaches point C? Ignore the effect of reflections from the walls, floor, and ceiling. Clearly explain your answer in terms of 2 c) Trung again stands against the right-hand wall at point o directly in front of the two speakers. If Trung starts walking toward corner C, how many minima will he hear before he reaches point C? Ignore the effect of reflections from the S₁ 不 2.00m 2.00m S₂ walls, floor, and ceiling. Clearly explain your answer in terms of Ar |

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**Problem TSN-3: Sound Waves from Two Speakers**

Two speakers, 4.00 meters apart, are positioned against the middle of one wall in a room that measures 10.0 meters by 30.0 meters. They produce sound with a wavelength of 0.900 meters.

**Problem a:**
Calculate the difference in path length for the waves from the two speakers that arrive at point C, located in the corner of the room to the right.

**Problem b:**
Trung is initially at point O, directly in front of the two speakers, against the right-hand wall. As Trung walks toward corner C, determine how many maxima he will hear after leaving point O and before reaching point C, ignoring the effects of reflections from walls, floor, or ceiling. Clearly explain your answer in terms of \(\frac{\Delta r}{\lambda}\).

**Problem c:**
Using the same setup, determine how many minima Trung will hear before reaching point C, under similar conditions of ignored reflections. Clearly explain your answer in terms of \(\frac{\Delta r}{\lambda}\).

**Diagram Explanation:**
- The diagram shows the room layout with the two speakers, \(S_1\) and \(S_2\), positioned 4.00 m apart.
- \(L_1\) and \(L_2\) are the paths from \(S_1\) and \(S_2\) to point C.
- The room dimensions are denoted with the width being 10.0 m to point C and a total height of 30.0 m. 
- Point O is on the right wall, 2.00 m above and below the speakers.

This exercise exemplifies wave interference patterns in a controlled environment, essential in understanding sound wave behavior.
Transcribed Image Text:**Problem TSN-3: Sound Waves from Two Speakers** Two speakers, 4.00 meters apart, are positioned against the middle of one wall in a room that measures 10.0 meters by 30.0 meters. They produce sound with a wavelength of 0.900 meters. **Problem a:** Calculate the difference in path length for the waves from the two speakers that arrive at point C, located in the corner of the room to the right. **Problem b:** Trung is initially at point O, directly in front of the two speakers, against the right-hand wall. As Trung walks toward corner C, determine how many maxima he will hear after leaving point O and before reaching point C, ignoring the effects of reflections from walls, floor, or ceiling. Clearly explain your answer in terms of \(\frac{\Delta r}{\lambda}\). **Problem c:** Using the same setup, determine how many minima Trung will hear before reaching point C, under similar conditions of ignored reflections. Clearly explain your answer in terms of \(\frac{\Delta r}{\lambda}\). **Diagram Explanation:** - The diagram shows the room layout with the two speakers, \(S_1\) and \(S_2\), positioned 4.00 m apart. - \(L_1\) and \(L_2\) are the paths from \(S_1\) and \(S_2\) to point C. - The room dimensions are denoted with the width being 10.0 m to point C and a total height of 30.0 m. - Point O is on the right wall, 2.00 m above and below the speakers. This exercise exemplifies wave interference patterns in a controlled environment, essential in understanding sound wave behavior.
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