Question

Sol. [Key Concept: Standing waves — harmonics in pipes]

For open organ pipe

- Number of nodes are same as number of harmonics

$$\ \therefore\ n = 5$$

For closed organ pipe

- There are only odd harmonics

For $1^{\text{st}\text{~}}$ harmonic → Number of nodes → 1

For $3^{\text{rd}\text{~}}$ harmonic → Number of nodes → 2

For $5^{\text{th}\text{~}}$ harmonic → Number of nodes → 3

For $7^{\text{th}\text{~}}$ harmonic → Number of nodes → 4

For $9^{\text{th}\text{~}}$ harmonic → Number of nodes → 5

$$\ \therefore\ m = 5 $$→ $\frac{n}{m} = \frac{5}{5} = 1$