Question

A cylindrical tube, open at both ends, has a fundamental frequency f in air . The tube is dipped vertically in water so that half of its length is in water. The fundamental frequency of the air column is now (a) f // 2 (b) 3 f // 4 (C ) f (d) 2f

Answer 1

Answer:

3f/c3b =/is 2f

Becausr it is the frequency of air

Answer 2

The fundamental frequency when one side closed in this case = f              (Option c)

Step by step explanation:

Given details,

Fundamental frequency in air = f Hz

Let the length of pipe = L m

Velocity of air = v ms⁻¹

$\textbf{\Large Formula of fundamental frequency }\\\text{(when both free sides )} = \frac{\textbf{\Large v}}{\textbf{\Large 2l}}$              (equation 1)

$\textbf{\Large Formula of fundamental frequency }\\\text{(when one side closed )} = \frac{\textbf{\Large v}}{\textbf{\Large 4l}}$             (equation 2)

Where l = Length of pipe

When the pipe is fully open the length of pipe = L

When the pipe is closed from one side (in case of tube half dipped in water)

the length of pipe = $\frac{L}{2}$

In first case when both sides are open

the fundamental frequency =$\frac{\textbf{\Large v}}{\textbf{\Large 2L}} = \textbf{\Large f}$

In second case when one side of pipe is closed

the fundamental frequency =$\frac{\textbf{\Large v}}{\frac{\textbf{\Large 4L}}{\textbf{\Large 2}} } = \frac{\textbf{\Large v}}{\textbf{\Large 2L} } = \textbf{\Large f}$

$\textbf{\Large So, the fundamental frequency when one side closed = f}\\ \\\textbf{\Large Option (C)}$