A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be 2.53 kHz. What is the speed of sound in steel?

Question

A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be 2.53 kHz. What is the speed of sound in steel? (A) 5 km / s (B) 6 km / s (C) 7 km / s (D) 4 km / s

Tardigrade Admin · Accepted Answer

In fundamental mode, l=2((λ/4))=(λ/2) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/a12db19d64f402f33d835f3f205dafd1-.png" /> ⇒ λ=2 l Given l=100 cm , v=2.53 kHz Using v=v λ ⇒ v=2.53 × 103 × 2 × 100 × 10-2 =5.06 × 103 m / s =5.06 km / s

Q. A steel rod $100 c m$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53 k Hz$ . What is the speed of sound in steel?

5 km / s

6 km / s

7 km / s

4 km / s

In fundamental mode,
$l = 2 (\frac{λ}{4}) = \frac{λ}{2}$

$\Rightarrow λ = 2 l$
Given $l = 100 c m, v = 2.53 k Hz$
Using $v = v λ$
$\Rightarrow v = 2.53 \times 1 0^{3} \times 2 \times 100 \times 1 0^{- 2}$
$= 5.06 \times 1 0^{3} m / s$
$= 5.06 km / s$

Q. A steel rod 100cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be 2.53kHz. What is the speed of sound in steel?