A sonometer is an audiometer used to measure hearing sensitivity and perform experiments related to the frequency of vibrating strings. It can demonstrate key physical relationships through three main experiments focusing on tension, frequency, length, and mass per unit length. The document outlines various methods to achieve resonance and explains the procedure for each experiment while emphasizing the importance of keeping certain variables constant.

1. SONOMETER
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By Aditya Abeysinghe

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3. ABOUT THE SONOMETER
Fixed bridge
Movable
bridge
Holes
Sonometer
string
PulleyWeight
Sonometer box
A sonometer is an audiometer which used to measure the
sensitivity of hearing. Several experiments about the
physical quantities and the relationships can be examined
using a sonometer

4. A tuning folk vibrating with a certain frequency is
introduced to the sonometer box and then the length
of the string or its tension is adjusted so that the
string also vibrates with the same frequency.
Since both the systems (tuning folk and the
sonometer) vibrate with the same frequency,
resonance takes place.
Resonance is the key to the experiments that we’ll
be doing shortly.
HOW DO SONOMETERS
WORK?

5. There are three methods by which a sonometer system
can be made to resonate:
1. Stationary wave method (Place paper strips between
the fixed and movable bridges. Then place the tuning
folk and adjust the distance between the two bridges
until paper strips fall of the string)
2. Beat method(Pluck the string between the two bridges.
Then keep the tuning folk and move away the movable
bridge until the no. of beats reach the minimum)
3. By listening to the change of frequencies(Listen to the
pitch of the sound emitted by the folk in air. Then pluck
the string between the two bridges and move the
movable bridge until you hear a similar pitch)
METHODS OF RESONATING A
SONOMETER SYSTEM

6. There are three main experiments that can be
performed using a sonometer:
1. To show that f α 1/l
2. To show that f α √T
3. To show that f α √1/m
Here T- Tension, f – frequency, l – length of string
used or length subjected to the experiment, m-
mass per unit length (mass/length)
EXPERIMENTS THAT CAN BE
PERFORMED USING A
SONOMETER

7. Note: To perform this experiment we have to keep the
tension and the mass per unit length constant.
From the formula,
f = (1/2l) (√T / m), we get l = (½ √T / m ) (1/f)
Method:
Arrange the sonometer and place some paper strips
between the two bridges. Then use the tuning folk beating
with the highest frequency and keep it on the sonometer
box. Then adjust the distance between the bridges so that
at some distance the papers fall. Then measure the length
between the bridges. Repeat the experiment with the other
folks in the sequence of deceasing order of their frequency
and record the minimum length required to remove the
strips off the string.
SHOWING THAT f α 1/l
y m x

8. Then plot the graph between l and 1/f.
If the graph is a straight line in the form of y=mx,
we can prove that l α 1/f or f α 1/l.
Then the gradient of that graph will be ½ √T / m .
However, we know that, √T / m = V, where V is the
velocity of sound in air.
Thus, the gradient of the graph,m = ½ V
Therefore, V = 2m.

9. Note: To perform this experiment we have to keep the
length and the mass per unit length constant.
From the formula,
f = (1/2l) (√T / m), we get f = ( ) √T
Method:
Arrange the sonometer and place some paper strips
between the two bridges. Then use the tuning folk beating
with the highest frequency and keep it on the sonometer
box.
SHOWING THAT f α √T
1
2l √m
y m x

10. Then keeping the distance between the bridges
constant, adjust the the tension, by adding mass,
and record the weight, or the tension, needed to
remove the paper strips off the string.Repeat the
experiment with the other folks in the sequence of
deceasing order of their frequency and record the
minimum tension, or the mass, required to remove
the strips off the string.
Then plot the graph between f and √T.
If the graph is a straight line in the form of y=mx, we
can prove that f α √T.

11. Note: To perform this experiment we have to keep the
length and the tension constant.
From the formula,
f = (1/2l) (√T / m), we get f = (√T / 2l) (1/ √m).
Method:
Arrange the sonometer and place some paper strips
between the two bridges. Then use the tuning folk
beating with the highest frequency and keep it on the
sonometer box.
SHOWING THAT f α 1 /√m
y m x

12. Then keeping the distance between the two bridges
the same, use different strings with various mass
per unit lengths and record the readings needed to
remove the paper strips off the string.. Repeat the
experiment with the other folks in the sequence of
deceasing order of their frequency and record the
value of m for different strings that are used to
remove the strips off the string.
Then plot the graph between f and √1/m.
If the graph is a straight line in the form of y=mx, we
can prove that f α √1/m.

13. *Note: We can also do this experiment by using
two strings connected parallely acrosses the two
bridges.
Then by changing the first string with some other
strings which have different m values, we can
measure the minimum length that is required in
the second string to be adjusted to make the
system resonate.