Question

A bucket kept under a running tap is getting filled with water. A person sitting at a distance is able to get an idea when the bucket is about to be filled.
(i) What changes take place in the sound to give this idea?
(ii )What causes the change in the sound?

Answer 1

Hint: An experience with acoustics is very critical in understanding the explanation for this sound behaviour. The sound pitch, which is generated and rises continuously, makes it shriller. The frequency depends on the depth of the bucket.

Complete step by step solution:
Sound frequency is the intensity of the sound's vibration which defines the quality of the sound. A frequency of \[1{\text{ Hz}}\] corresponds to one wave cycle per second, while \[20{\text{ Hz}}\] corresponds to \[20\] per second, where the periods are \[20\] times smaller and nearer together.

(i) When the length \[l\] of the air column is reduced, i.e. when the bucket is filled with water, the frequency of sound may increase as \[f \propto \dfrac{1}{l}\].

Here the bucket is presumed to be closed at one end to a (organ) pipe. Now, it would give the frequency of the basic node generated by the bucket as
\[n = \dfrac{v}{{4L}}\]
So, the frequency obviously depends on the length of the bucket or tubing. Now, as the water begins to fill in, in compliance with the above relationship, the duration \[L\] decreases, which thereby raises the frequency \[n\] of the sound produced. This rise in frequency is the rise in the pitch of sound created by dropping water, and when the bucket is on the verge of being fully loaded, the pitch will be the highest.

(ii) Shift in sound is caused by a reduction throughout the air column as the water in the bucket is filled. The length of the air column reduces as the water level in the bucket grows past the running tap, so the volume of sound created increases i.e. the sounds gets shriller and meaner.

Note: In order to answer this question we must have the knowledge of sound and its relation with the frequency. Know that frequency of sound is related to the length or the depth. This rise in frequency is the rise in the pitch of sound created by dropping water, and when the bucket is on the verge of being fully loaded, the pitch will be the highest.