Question

the fundamental mode, time taken by the wave to reach the closed end of the air filled pipe is 0.01 s. The fundamental frequency is

Answer 1

25 Hz

Answer 2

For a pipe closed at one end, the fundamental mode has a length equal to one‐quarter of the wavelength:

$$L=\frac{\lambda}{4}$$

The time $t$ taken by the wave to travel from the open end to the closed end gives:

$$L = vt$$

Thus,

$$\lambda = 4vt$$

The frequency is given by:

$$f=\frac{v}{\lambda} = \frac{v}{4vt} = \frac{1}{4t}$$

Substitute $t=0.01$ s:

$$f = \frac{1}{4(0.01)} = \frac{1}{0.04} = 25\,\text{Hz}$$

Explanation:

• For a closed pipe, $L=\lambda/4$.
• $L = v(0.01)$.
• Thus, $f = 1/(4(0.01)) = 25$ Hz.