SONOMETER

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By Aditya Abeysinghe

SEE THE VIDEO FORMAT OF THIS PRESENTATION AT:

https://www.youtube.com/watch?v=HYBErJgAbFg

See more of my videos at :https://www.youtube.com/channel/UCVFSs7LUN4DSr0a4kkGt4Ag

ABOUT THE SONOMETER

Fixed bridge Movable bridge

HolesSonometer 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

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?

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

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

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

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.

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

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.

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

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.

*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.