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

# A one-metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be - Physics

Sum

A one-metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops?

#### Solution

Given:
Length of the stretched string (L) = 1.00 m
Mass of the string =40 g
String is attached to the tuning fork that vibrates at the frequency (f) = 128 Hz
Linear mass density (m)
$= \left( 40 \times {10}^{- 3} \right) kg/m$
No. of loops formed, (n) = 4

$L = \frac{n\lambda}{2}$

$\Rightarrow \lambda = \frac{2L}{n} = \frac{2 \times 1}{4}$

$\Rightarrow \lambda = 0 . 5 m$

Wave  speed  $(v) = f\lambda = 128 \times 0 . 5$

$\Rightarrow v = 64 m/s$

$We know:$

$v = \sqrt{\left( \frac{T}{m} \right)}$

$\Rightarrow T = \nu^2 m$

$= \left( 64 \right)^2 \times 40 \times {10}^{- 3}$

$= 163 . 84 \approx 164 N$
Hence, the tension in the string if it is to vibrate in four loops is 164 N.

Concept: Speed of Wave Motion
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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 15 Wave Motion and Waves on a String
Q 40 | Page 326