Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# A Sonometer Wire Supports a 4 Kg Load and Vibrates in Fundamental Mode with a Tuning Fork of Frequency 416. Hz. the Length of the Wire Between the Bridges is Now Doubled. - Physics

MCQ

A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416. Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to

• 1 kg

• 2 kg

• 8 kg

• 16 kg.

#### Solution

16 kg

According to the relation of the fundamental frequency of a string
$\nu = \frac{1}{2l}\sqrt{\frac{F}{\mu}}$
where l is the length of the string
is the tension
μ is the linear mass density of the string
We know that ν1 = 416 Hz, l1 = l and l2 = 2l.
Also, m1 = 4 kg and m2 = ?
$\nu_1 = \frac{1}{2 l_1}\sqrt{\frac{m_1 g}{\mu}}.................. (1)$
$\nu_2 = \frac{1}{2 l_2}\sqrt{\frac{m_2 g}{\mu}} (2)$
So, in order to maintain the same fundamental mode
$\nu_1 = \nu_2$
squaring both sides of equations (1) and (2) and then equating

$\frac{1}{4 l^2}\frac{4g}{\mu} = \frac{1}{16 l^2}\frac{m_2 g}{\mu}$

$\Rightarrow m_2 = 16 kg$

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 15 Wave Motion and Waves on a String
MCQ | Q 22 | Page 323