What is Sonometer?
A sonometer is defined as
The device that is used for demonstrating the relationship between the frequency of the sound that is produced by the string when it is plucked and the tension, length, and mass per unit length of the string.
The sound is produced in the transverse standing wave in the string.
Sonometer Diagram
Construction of Sonometer
- A hollow box of one meter long is used for making the sonometer.
- This hollow box consists of a uniform metallic string attached to it.
- The first end of the string is connected to the hook while the second end is connected to the weight hanger with the help of a pulley.
- The number of strings used is one and therefore, it is also known as the monochord.
- In order to increase the tension of the string, weights are added at the free end.
- To change the vibrating length of the string which is stretched, two adjustable knives are placed and their positions are adjusted accordingly.
Working of Sonometer
Once the set-up is done (as shown in the sonometer diagram), a transverse standing wave is produced at the edges of the knives with the nodes. Along with the nodes, there is a formation of the anti-nodes.
The mathematical explanation to the working of the sonometer is as follows:
Let l be the length of the vibrating element
l = λ/2
λ = 2l
Let f be the frequency of the vibrating element. T be the tension created in the string and μ be mass per unit length. Then,
If ⍴ is the density of the material and d is the diameter of the string, the mass per unit length μ is given as
μ = area x density = πr2⍴ = π⍴d2/4
Then frequency is
Laws of Transverse Vibrations
The laws of transverse vibrations on a stretched string can be divided into two laws, and they are:
- Law of length
- Law of tension
- Law of mass
Law of Length
The law of length states that the frequency of the vibration of a stretched string and its resonating length varies inversely as long as the mass per unit length and the tension of the string is constant.
F ∝ 1/l
Law of Tension
The law of tension states that the frequency of vibration of a stretched string and the square root of its tension varies directly as long as the resonating length and the mass per unit length of the string is constant.
F ∝ √T
Law of Mass
The law of mass states that the frequency of vibration of a stretched string and the square root of its mass per unit length varies inversely proportional as long as the length and the tension is constant.
F ∝ 1/√m
What is the use of sonometer?
We already know that the sonometer is used for demonstrating the relationship between the frequency and the tension, length, and mass per unit length of the string. Therefore, the following can be determined using a sonometer:
- The frequency of the tuning fork
- The frequency of the alternating current
- The tension in the string
- The unknown mass of the object hanging down
Stay tuned with BYJU’S to learn more about other concepts of Physics.
Frequently Asked Questions – FAQs
What is an example of a standing wave?
An example of a standing wave is noticed in stringed musical instruments.
What is meant by a standing wave?
A standing wave is a combination of two waves moving in opposite directions such that they have the same amplitude and frequency and is obtained due to interference. The standing wave is also known as the stationary wave.
Why are holes kept on one side of the sonometer box?
The holes in the sonometer box act as a way through which the frequency of vibration of the string is communicated inside the hollow portion of the box.
Which material is used for sonometer wire?
The wire that is used in the sonometer is soft iron.
Who invented sonometer?
The first monochord was invented by Pythagoras in the 7th century. Later in the mid 1800, Albert Marloye, a French instrument maker, modified the monochord into a differential sonometer.
Audible and Inaudible Sounds
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