Question

An empty vessel is filled with water, its fundamental frequency
A. Increases
B. Decreases
C. Remains the same
D. None of these

Answer 1

Use the formula for the fundamental frequency of the sound in a closed organ pipe. This formula gives the relation between the fundamental frequency of the sound in the organ pipe, velocity of the sound wave and length of the organ pipe. This formula gives the relation between the fundamental frequency and length of the organ pipe. Hence, determine filling the water in the organ pipe increases or decreases the frequency.

Formula used:
The fundamental frequency $n$ of in a closed organ pipe is given by
$n = \dfrac{v}{{4L}}$ …… (1)
Here, $v$ is the velocity of the sound in the organ pipe and $L$ is the length of the organ pipe.

Complete answer:
From the equation (1), we can conclude that the fundamental frequency of the sound in a closed organ pipe is directly proportional to the velocity of the sound wave in the organ pipe and inversely proportional to length of the organ pipe.
$n \propto \dfrac{v}{L}$

In a closed organ pipe, the air molecules in the air column are set into vibrations. The amplitude of vibration of the air molecules is greater than the amplitude of vibration of the liquid molecules.This affects the velocity of the sound wave in the organ pipe.Also when the organ pipe is filled with water, the length of the organ pipe decreases.

Since the frequency of the sound in the organ pipe is inversely proportional to length of the air column. Hence, the decrease in length of the air column increases the frequency of the sound in the organ pipe.Therefore, when the organ pipe is filled with water, the frequency of the sound produced increases.

Hence, the correct option is A.

Note: The students may think that the velocity of the sound wave decreases when the water is filled in the organ pipe. So, why does the fundamental frequency increase when the water is filled. But the students should keep in mind that the decrease in velocity of the sound is less as compared to decrease in length of the air column. Hence, the frequency of the sound increases when the water is filled in the organ pipe.