The Question is from NEET guide , and it was created by the author ABDUL JILANI BASHA

Question

Which of the following factors does NOT affect the fundamental frequency of a vibrating sonometer wire?

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: 3
## CONCEPT FRAMEWORK
 **Primary Concept**: Fundamental frequency of a vibrating string
 **Related Topics**: Waves, resonance, standing waves
 **Prerequisites**: Understanding of wave properties, frequency, tension, and the relationship between them.
## SOLUTION PATHWAY
**Given Information**:
The question asks which factor does NOT affect the fundamental frequency of a vibrating sonometer wire.
**Method & Steps**:
The fundamental frequency ($f$) of a vibrating string is given by the formula:
1. $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$
where:
* $L$ is the length of the wire
* $T$ is the tension in the wire
* $\mu$ is the linear mass density of the wire ($\mu = \frac{m}{L}$, where $m$ is the mass of the wire)
2.  Analyzing the formula, we see that the frequency is directly proportional to the square root of the tension ($T$) and inversely proportional to the length ($L$) of the wire. The linear mass density ($\mu$) is related to the mass and length of the wire, and also incorporates the diameter (since mass is proportional to volume, which depends on diameter). The material of the wire determines its density, which directly affects the linear mass density ($\mu$).
3. Therefore, the length, tension, and material of the wire (through its effect on linear mass density) affect the fundamental frequency.  However, while the diameter influences the mass and hence the linear mass density, it is not an independent factor in the formula itself.
**Result**: The diameter of the wire does not directly appear in the formula. Changes in diameter affect the mass and hence linear density, which is already accounted for in the formula.
**Verification**: The formula shows a clear dependence on length, tension, and linear mass density (which is affected by material and diameter). Diameter's impact is indirect and already considered through linear mass density.
## OPTION ANALYSIS
A :x: Length affects the fundamental frequency (inversely proportional).
B :x: Tension affects the fundamental frequency (directly proportional).
C ✓: Diameter does not directly appear in the formula. Its effect is indirect through the linear mass density.
D :x: Material affects the linear mass density, hence affecting the fundamental frequency.
## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing the direct and indirect relationship of diameter:  Students might incorrectly think diameter directly impacts frequency, neglecting its influence through the linear mass density.
  2. Forgetting the role of linear mass density:  Students might overlook the importance of the linear mass density in the formula and incorrectly exclude the material's effect.
 **Quick Tips**:
  1. Memorize the formula and understand each variable's role.
  2. Visualize a thicker wire having more mass, thus affecting the frequency through changing the linear mass density.

ABDUL JILANI BASHA · Answer

Length of the wire

ABDUL JILANI BASHA · Answer

Tension in the wire

ABDUL JILANI BASHA · Answer

The correct Option is "Diameter of the wire"

ABDUL JILANI BASHA · Answer

Material of the wire

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