Question

8. The fundamental frequency of a closed end pipe is 480
Hz what is the fundamental note when its1/4 Th
length is filled with water?
a) 120 Hz
c) 960 Hz
b) 240 Hz
d) 640 Hz

Answer 1

The fundamental frequency of a pipe closed at one end is

The fundamental frequency of a closed end pipe is 480. Hz what is the fundamental note when its1/4 Th

Answer 2

Answer:

The fundamental note when its1/4 th length is filled with water is 640Hz i.e.option(d).

Explanation:

The fundamental frequency of closed-end pipe is given as,

$f=\frac{v}{4l}$               (1)

Where,

F=fundamental frequency

v=velocity of the sound

l=length of the closed-end pipe

The fundamental frequency given in the question is  480Hz.

So,

$480=\frac{v}{4l}$          (2)

When it is filled with water then the frequency will become,

$f'=\frac{v}{4l'}$        (3)

Where,

f'=new frequency in water

l'=length of the pipe available after filling with water

Now,

$l'=l-\frac{l}{4}$     (∵as 1/4 th length is filled with water)

$l'=\frac{3l}{4}$             (4)

By using equation (4) in equation (3) we get;

$f'=\frac{v}{4\times \frac{3l}{4}}=\frac{v}{4l}\times \frac{4}{3}=f\times \frac{4}{3}$          (using equation (1))

$f'=480\times \frac{4}{3}=640Hz$                  (using equation (2))

Hence, the fundamental note when its1/4 th length is filled with water is 640Hz i.e.option(d).