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An experiment is conducted to determine the speed of sound $(v)$ in air using a resonance column. The column is filled with a known liquid, and a tuning fork of known frequency (f) is used. The first resonance occurs at a column height $(h)$ of $25\ cm$ , and the second resonance occurs at $75\ cm$ . Calculate the speed of sound in air.
Option: 1
$100\ m/s$

Option: 2
$235\ m/s$

Option: 3
$169\ m/s$

Option: 4
$128\ m/s$

Answers (1)

best_answer

Given values:
• Frequency of tuning fork $(f)=256\ Hz$
• First resonance height $(h_1)=25\ cm$
• Second resonance height $(h_2)=75\ cm$

The speed of sound (v) can be calculated using the formula for the funda-
mental frequency of an open-open resonance column:

$v=2 h_1 f$

Step 1: Calculate the speed of sound (v) using the first resonance height and
frequency:

$v=2 \times 25 \mathrm{~cm} \times 256 \mathrm{~Hz}$

Step 2: Calculate v:

$v=12800\ cm/s$
The speed of sound in air is $12800\ cm/s$ .
Step 3: Convert the speed of sound to $m/s$ .
$v=128\ m/s$
The speed of sound in air is $128\ m/s$ .
Therefore, the correct option is (D).

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