Fundamental frequency of a sonometer wire is n. If the length and diameter of the wire are doubl

Name: Problem 1491, Chapter 10: JEE Physics
Uploaded: 2021-11-28T11:55:39-08:00
Duration: 1 min 27 s
Channel: Akshaya Rs
Description: Fundamental frequency of a sonometer wire is n. If the length and diameter of the wire are doubled keeping the tension same, the new fundamental frequency is...... (A) (2 n / √(2)) (B) {n /(2 √(2)) (C) √(2 n) (D) (n / 4)

step 1 Hello everyone in this question we will be understanding some basic concepts of the oscillation

Question

Fundamental frequency of a sonometer wire is $\mathrm{n}$. If the length and diameter of the wire are doubled keeping the tension same, the new fundamental frequency is...... (A) $(2 \mathrm{n} / \sqrt{2})$ (B) $\{\mathrm{n} /(2 \sqrt{2})$ (C) $\sqrt{2 n}$ (D) $(\mathrm{n} / 4)$

   Fundamental frequency of a sonometer wire is $\mathrm{n}$. If the length and diameter of the wire are doubled keeping the tension same, the new fundamental frequency is......
(A) $(2 \mathrm{n} / \sqrt{2})$
(B) $\{\mathrm{n} /(2 \sqrt{2})$
(C) $\sqrt{2 n}$
(D) $(\mathrm{n} / 4)$

JEE Physics

StemEZ 1st Edition

Chapter 10, Problem 1491

Instant Answer

Solved by Expert Akshaya Rs

11/28/2021

Step 1

Step 1: The fundamental frequency of a sonometer wire is given by the formula: \[n = \frac{1}{2L} \sqrt{\frac{T}{\mu}}\] where $L$ is the length of the wire, $T$ is the tension in the wire, and $\mu$ is the linear mass density of the wire. Show more…

Show all steps

Thanks for your feedback!

Fundamental frequency of a sonometer wire is $\mathrm{n}$. If the length and diameter of the wire are doubled keeping the tension same, the new fundamental frequency is...... (A) $(2 \mathrm{n} / \sqrt{2})$ (B) $\{\mathrm{n} /(2 \sqrt{2})$ (C) $\sqrt{2 n}$ (D) $(\mathrm{n} / 4)$

Play audio

Feedback

Akshaya Rs and 100 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Fundamental Frequency of a Stretched String

This concept refers to the lowest possible frequency at which a stretched string vibrates, determined by the equation f = (1/2L)?(T/?), where L is the length of the string, T is the tension, and ? is the mass per unit length. It shows that the frequency is inversely proportional to the length of the string and is influenced by both the tension and the string's linear density.

Effect of Wire Geometry on Linear Density

The linear density (?) of a wire is dependent on its mass per unit length, which in turn is proportional to the cross-sectional area of the wire. When the diameter of the wire is doubled, the cross-sectional area, and therefore the mass per unit length, increases by a factor of four. This change directly impacts the frequency of vibration, as an increased ? leads to a decrease in the fundamental frequency for a given tension.

Please give Ace some feedback