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{:(,"Column I",,"Column II"),((A),"A str...

`{:(,"Column I",,"Column II"),((A),"A stretched string",(p),"n antinodes"),((B),"Open organ pipes",(q),"n nodes"),((C),"Closed organ pipe",(r),"(n + 1) antinodes"),((D),"A stationary wave produced",(s),"(n + 1) nodes"),(,"in organ pipes may have",,):}`

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To solve the problem of matching the items in Column I with those in Column II, we will analyze each item in Column I and determine the corresponding item in Column II based on the properties of standing waves in different mediums. ### Step-by-Step Solution: 1. **A Stretched String**: - A stretched string fixed at both ends will have nodes at the ends and antinodes in between. - The number of nodes (N) is given by N = n + 1, where n is the number of loops or antinodes. - Therefore, for a stretched string, there are **n antinodes** and **n + 1 nodes**. - **Match**: A → S (n + 1 nodes). 2. **Open Organ Pipes**: - Open organ pipes are open at both ends, which means there are antinodes at both ends. - The number of nodes (N) is given by N = n, where n is the number of loops or antinodes. - Therefore, for open organ pipes, there are **n + 1 antinodes** and **n nodes**. - **Match**: B → R (n + 1 antinodes) and B → Q (n nodes). 3. **Closed Organ Pipe**: - A closed organ pipe has one end closed, which means there is a node at the closed end and an antinode at the open end. - The number of nodes (N) is given by N = n, where n is the number of loops or antinodes. - Therefore, for a closed organ pipe, there are **n antinodes** and **n nodes**. - **Match**: C → P (n nodes) and C → Q (n nodes). 4. **A Stationary Wave Produced in Organ Pipes**: - Stationary waves in organ pipes can have various configurations depending on whether the pipe is open or closed. - The combinations can include both n nodes and n + 1 antinodes. - Therefore, the possible matches are **n + 1 antinodes** and **n nodes**. - **Match**: D → R (n + 1 antinodes) and D → Q (n nodes). ### Final Matches: - A → S (n + 1 nodes) - B → R (n + 1 antinodes) and B → Q (n nodes) - C → P (n nodes) and C → Q (n nodes) - D → R (n + 1 antinodes) and D → Q (n nodes)

To solve the problem of matching the items in Column I with those in Column II, we will analyze each item in Column I and determine the corresponding item in Column II based on the properties of standing waves in different mediums. ### Step-by-Step Solution: 1. **A Stretched String**: - A stretched string fixed at both ends will have nodes at the ends and antinodes in between. - The number of nodes (N) is given by N = n + 1, where n is the number of loops or antinodes. - Therefore, for a stretched string, there are **n antinodes** and **n + 1 nodes**. ...
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