1) Aim
2) Apparatus
3) Diagram
4) Formula with explanation/law
5) Theory
6) Observations
7) Observation Table
8) Calculation
9) Result/Conclusion
10) Precautions
11) Questions
12) Graph
आता आपण Experiment चे Solutions पाहण्यास सुरुवात करुया :-
Class 12 Physics Practical No 4 : Sonometer Law of Length Solutions Maharashtra Board
[Page No 35]
Aim :
To study the relationship between frequency and length of a given wire under constant tension using sonometer.
Apparatus :
Sonometer, slotted weights with hanger, set of tuning forks, rubber pad, light paper rider, meter scale.
Diagram :
Theory :
Law of Length : The frequency of stationary transverse vibrations of a stretched string is inversely proportional to its vibrating length when the tension and mass per unit length of the wire are kept constant.
Thus n*α*1/l
∴ nl = constant when T and m are constant.
Formula :
n = 1/2l*√T/m
Where,
n = frequency of vibration of the wire.
T = tension applied to the wire.
m = mass per unit length of the wire
l = vibrating length of the wire.
[Page No 36]
Observations :
1) Mass of the hanger M0 = 500g Total mass M = 1500
2) Tension applied to the wire T = 1500 * 980 dyne.
To measure vibrating length :
| Obs.No. | Frequency of tuning fork n Hz |
Vibrating length of the wire | 1/l | nl Hz-cm |
||
|---|---|---|---|---|---|---|
| l1 | l2 | Mean l cm | ||||
| 1 | x | 10.9 | 11.0 | 10.95 | 0.09128 | 5597 |
| 2 | 480 | 12.4 | 12.5 | 12.45 | 0.08032 | 5974 |
| 3 | 426 | 14.3 | 14.4 | 14.35 | 0.06969 | 6549 |
| 4 | 384 | 14.8 | 14.9 | 14.85 | 0.06733 | 5703 |
| 5 | unknown n'=320 | 18.2 | 18.3 | l'=18.25 | 0.05480 | 5853 |
Calculations :
To find nl
| Obs.No. | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Log n=a | 2.7084 | 2.6812 | 2.6294 | 2.5843 | 2.5051 |
| Log l=b | 1.0395 | 1.0951 | 1.1568 | 1.1718 | 1.2613 |
| a+b=c | 3.7479 | 3.7763 | 3.8162 | 3.7561 | 3.7664 |
| Antilog c=nl | 5597.0 | 5974.0 | 6549.0 | 5703.0 | 5853.0 |
Mean (nl) = 5955.75
Unknown frequency n' = Hz (nl)mean/l' = 326 Hz.
[Page No 39]
Result :
1) nl = 5955 = constant, when T and m are kept constant, Hence law of Length is verified.
2) The graph of reciprocal of vibrating length against frequency of vibrations of wire is straight line. Hence n ∝ 1/l
3) unknown frequency of tuning fork by calculation n' = 326 Hz
4) Unknown frequency of tuning fork by graph n' = 325 Hz
Precautions :
i) Place the paper rider mid - way between knife edges.
ii) Paper rider should be light and dry.
iii) Strike tuning fork on the rubber pad gently.
iv) Place the stem of the vibrating tuning fork gently on the sonometer box.
v) Measure the distances between the knife - edges accurately.
Questions :
1) State the law of Length of vibrating string.
Ans : The law of the length of a vibrating string states that the frequency of vibration of a string is inversely proportional to its length, given the tension and mass per unit length remain constant. Mathematically, the relationship is expressed as f ∝ 1/L, where f is the frequency of vibration and L is the length of the string.
2) What is fundamental mode of vibration?
Ans : The fundamental mode of vibration is the simplest and lowest frequency pattern of vibration in a vibrating system, where the entire system vibrates as a single entity with the lowest possible number of nodes and antinodes. It represents the primary resonance of the system and is often the most prominent and easily observable mode of vibration.
3) What is resonance?
Ans : Resonance is a phenomenon that occurs when an external force or frequency matches the natural frequency of a system, resulting in a significant increase in amplitude or vibration, often leading to enhanced oscillations or vibrations. In such cases, small periodic forces can cause large and sustained responses, making resonance crucial in understanding various physical, mechanical, and electrical systems.
4) What is forced vibrations?
Ans : Forced vibrations occur when an external periodic force or driving force is applied to a system, causing it to vibrate at a frequency determined by the external force rather than its natural frequency.
These vibrations can lead to significant amplitude and are commonly observed in mechanical systems driven by periodic forces like engines, musical instruments, and machinery.
5) Explain why holes are kept on one side of sonometer box?
Ans : Holes are kept on one side of the sonometer box to allow the sound produced by the vibrating string to escape and propagate freely, ensuring accurate measurements of sound frequencies and minimizing sound reflections that could interfere with the experiment.
Graphs :
A graph of 1/l against n
अशा प्रकारे मित्रांनो आपण इयत्ता बारावी Physics Practical Number 4 - Sonometer Law of Length याचे Solutions पहिले.
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