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Sonometer is a device which is used to measure sound related measurements. It is used for the demonstration of the relationship between the frequency of sound produced by a string and the length, tension and mass per unit length of the same string.
- Sonometer works on the principle of the Law of Tension.
- String produces the sound in the transverse standing waves.
- It is used both in tuning musical instruments and producing music.
- It is also used by the scientists in Physics laboratories.
Read More: NCERT Solutions for class 11 Physics Waves
Key Terms: Sonometer, Sound, Frequency, Transverse Vibration, String, Laws of Transverse Vibrations, Tension
What is Sonometer?
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A sonometer is a device that is used to measure the relationship between the frequency of the sound produced by a plucked string, and the tension, length and mass per unit length of the string.
Sonometer
Sonometers are also used to measure the following:
- Frequency of the tuning fork or frequency of the alternating current.
- Unknown hanging masses.
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Construction of Sonometer
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Sonometeers can be constructed as follows:
- A sonometer basically consists of a hollow rectangular wooden box.
- The wooden box consists of a one-meter-long uniform metallic thin string which is attached to it.
- One end of the string is attached to a hook and the other end is connected to a weight hanger through a pulley as shown in the below figure, this is also known as monochord.
- The weights added to the free end of the wire is to increase the tension of the wire.
- There are two adjustable wooden knives that are put over the board and their positions are adjusted to change the vibrating length of the stretched wire.
Construction of Sonometer
Working of Sonometer
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Once the set-up of a sonometer is completed, a transverse standing wave is produced at the knife edges with the nodes. There is a formation of the anti-nodes along with the nodes.
The mathematical explanation of the working of the sonometer is as follows:
Let
- l be the length of the vibrating element.
- f be the frequency of the vibrating element.
- T be the tension created in the string.
- μ be mass per unit length.
Then,
If ρ 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. Then, the frequency is
Read More: Relationship Between Frequency and Length of Wire
Uses of Sonometer
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Sonometer is a device which is used to measure the relationship between the frequency of the sound produced by a plucked string, and the tension, length and mass per unit length of the string. The sound is produced in a transverse standing wave in the string. The sound produced is in nodes or antinodes.
There are following applications wherein the sonometer is used:
- To find the frequency of the tuning fork.
- To validate the transverse laws.
- To use in finding the tension of the vibrating string.
- To find and hear the sensitivity.
- To determine bone density.
Read More: Waves Important Questions
Laws of Transverse Vibrations
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There are three laws of transverse vibration of string on a stretched string:
- Law of Length
- Law of Tension
- Law of Mass
Law of Length
As per the first law, the frequency of a stretched string's vibration and its resonating length fluctuates inversely as long as the mass per unit length and the tension of the string is constant.
f ∝ 1/length
Law of Tension
As per the second law, the frequency of vibration of a stretched string and the square root of its tension fluctuates directly as long as the resonating length and the mass per unit length of the string is constant.
f ∝ 1√T (Tension)
Law of Mass
As per the third law, a stretched string's frequency of vibration and the square root of its mass per unit length varies inversely proportionally when the length and tension are both constant.
f ∝ 1/√mass(m)
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Things to Remember
- Sonometer is used to show the connection between and the tension, length, and mass per unit length of the string and frequency.
- Albert Marloye, a French instrument maker, modified the monochord into a sonometer.
- Sonometer is used to determine the tuning fork frequency, alternating current frequency, ‘tension of the string’, and the unknown hanging masses.
- It is also used in medical settings to test both hearing and bone density.
- There are three Laws of Transverse Vibrations namely Law of Length, Law of Tension, and Law of Mass.
Previous Years’ Questions
- The length of a sonometer wire AB is 110 cm. Where should… (JIPMER - 2016)
- In an experiment with sonometer a tuning fork of frequency… (BITSAT - 2005)
- The total length of a sonometer wire between fixed ends… (JEE Main - 2014)
- A sonometer wire of length 114cm is fixed at both the ends… (JEE Main - 2013)
- Fundamental frequency of a sonometer wire is n. If the… (UPSEE - 2015)
- In a sonometer experiment, when the tension is changed… (COMEDK UGET - 2010)
- The frequency of a sonometer wire is 100 Hz. When the… (BITSAT - 2015)
- A 70cm long sonometer wire is in unison with a tuning fork… (AMUEEE - 2014)
- A sonometer wire resonates with a given tuning fork forming… (BITSAT - 2017)
- The distance between the two successive nodes is… (Manipal - 2013)
Sample Questions
Ques. What is a Sonometer? (2 Marks)
Ans. A sonometer is a device that is used to measure the relationship between the frequency of the sound produced by a plucked string, and the tension, length and mass per unit length of the string. The following quantities can be determined using sonometer such as:
- For tuning the fork frequency or frequency of the AC (Alternating current)
- The unknown hanging masses
Ques. What are the uses of sonometer? (2 Marks)
Ans. Sonometer is used to measure the relationship between the frequency of the sound produced by a plucked string, and the tension, length and mass per unit length of the string. There are following further uses of sonometer:
- The frequency of the tuning fork
- The frequency of the alternating current
- The unknown hanging masses
Ques. What is the function of a sonometer? (2 Marks)
Ans. Sonometer uses the principle of Resonance. It is a device which is used to measure the relationship between the tension, length and mass per unit length of the string with the frequency of the sound produced by a plucked string.
Ques. What are the examples of a sonometer in daily life? (2 Marks)
Ans. A sonometer is a device which is used by the string at the time of plucking for defining the intricate relationship that exists between the frequencies for the sound produced. Also, it is used for diagnostic purposes such as to measure the tension, frequency and density. They are even used in medical settings to test both hearing and bone density.
Ques. Which is the principle of the sonometer? (3 Marks)
Ans. The sonometer is a device which works on the principle of resonance. Resonance is a phenomenon in which an external force or force vibration is produced in sound waves.
- It is a device which tends to vibrate at the resonant frequency with a larger amplitude.
- If a tuning fork is kept near the sonometer the air which is in the hollow wooden box starts vibrating and the string goes into resonance at a specific length depending upon the tuning fork.
- The vibrating string is used to determine the tuning fork frequency.
Ques. What is meant by a Standing Wave? (2 Marks)
Ans. Standing Wave is also known as a stationary wave which is a combination of two waves which are moving in the same direction with same amplitude and frequency. This phenomenon is due to the result of interference. These are characterized by nodes and antinodes. The amplitude of vibration is maximum at the antinode and minimum at the node.
Ques. What does the law of tension convey? (2 Marks)
Ans. As per the law of tension, if we take l as length and v is the vibration of string, the prime frequency of vibrations of the respective string is directly proportional to the square root of tension, at a constant length of vibration and mass per unit length. It is expressed as v∝1/l.
Ques. What do you mean by pitch and what are the factors affecting it? (2 Marks)
Ans. Pitch of a sound is basically our ear’s response to the frequency of vibrations. If the frequency of the vibration is higher then we say that his sound is high whereas if the sound is said to have a lower pitch, then the frequency of vibration is low.
The factors on which the pitch of sound depends upon are:
- Frequency
- Wavelength
- Time Period
Ques. A sonometer of wire of length 100 cm is stretched by a weight of 1000g. The fundamental frequency of vibration is 100Hz. Calculate the linear density of the wire. (2 Marks)
Ans. Given
- l = 100 cm = 1m
- T = 1000g = 1 kg = 1 x 9.8 = 9.8N. n = 100Hz
We know now that
Therefore, linear density m = T/ 4l2n2
m = 9.8/ 4 x (1)2 x (100)2
m = 245 x 10-6 k kg/m
Ques. There is a wire of length 100m and a weight of 2kg is attached at one end of the string. If the frequency of vibration is 100 Hz, then what is the linear density ρ? (2 Marks)
Ans. Given that
- Length of the wire = 100m
- Fundamental frequency v = 100Hz
- ρ =?
We know that
Where T is the tension in the string, t = mg = 2 x 9.8 N = 19.6N
From (1) squaring both sides, and inserting the above values, we get:
ρ = 19.6 / 4 x 100 x 100 x 100 x 100
ρ = 4.9 x 10-8 kg m-1
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