Question

As an empty vessel is filled with water, its fundamental frequency
A. Increases
B. Decreases
C. Remains unchanged
D. None of these

Answer 1

An empty vessel with a base will be acting like a closed organ pipe. The fundamental frequency can be found by taking the ratio of the velocity of sound to the four times of length of the air column in the pipe. Hence the fundamental frequency ${{n}_{1}}$​ will be increased as length of the air column and fundamental frequency will be inversely proportional to each other. This will help you in answering this question.

Complete step by step solution:
An empty vessel with a base will be like a closed organ pipe. And the fundamental frequency of a closed organ pipe can be written as,
${{n}_{1}}=\dfrac{V}{4l}$
Where $l=$length of air column in pipe (height of pipe) and $V$ be the velocity of sound.

From the above equation we can write that,
${{n}_{1}}\propto \dfrac{1}{l}$

When we fill the empty vessel with water, the length of the air column $l$ in the pipe will get decreased and hence the fundamental frequency ${{n}_{1}}$​ will be increased as length of the air column and fundamental frequency will be inversely proportional to each other.

When the length of the air column increases, the fundamental frequency decreases. Similarly when the length of the air column is decreased, fundamental frequency is increased.

Therefore the correct answer has been obtained as option A.

Note:
The organ pipe which is made as one end is kept open and another end is closed is known as closed organ pipe. Bottle and whistle are some examples of closed organ pipes. The organ pipe which is made as both of its ends kept open is referred to as an open organ pipe. Flutes are the example of open organ pipes.