A pipe 20cm long is closed at one end. Which harmonic mode of th epipe is resonantly excited by a 430Hz source? Will the same source be in resonance with the pipe if both ends are open? Take speed of sound in air `340m//s`.

Explanation

To solve the problem, we need to determine the harmonic mode of a closed-end pipe that resonates with a 430 Hz source and whether the same source will resonate with a pipe that is open at both ends. We will use the speed of sound in air, which is given as 340 m/s, and the length of the pipe, which is 20 cm (or 0.2 m).

### Step-by-Step Solution:

**Step 1: Determine the fundamental frequency of the closed-end pipe.**
- The formula for the fundamental frequency (first harmonic) of a closed-end pipe is given by:
\[
f_1 = \frac{v}{4L}
...