# A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will - Physics

MCQ

A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will

#### Options

•  vibrate with a frequency of 416 Hz

•  vibrate with a frequency of 208 Hz

•  vibrate with a frequency of 832 Hz

• stop vibrating.

#### Solution

vibrate with a frequency of 208 Hz

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

We know that ν1 = 416 Hz, l1 = and l2 = 2l.
$v_1 \propto \frac{1}{l_1}$
$v_1 l_1 = v_2 l_2$
$\left( 416 \right)l = v_2 \left( 2l \right)$
$v_2 = 208 Hz$

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 21 | Page 323