Question

In a resonance tube with tuning fork of frequency, $512Hz$, first resonance occurs at water level equal to $30.3$ cm and second resonance occurs at $63.7$ cm. The maximum possible error in the speed of sound is

• A. $51.2cm/s$
• B. $102.4cm/s$
• C. $204.8cm/s$
• D. $153.6cm/s$

Answer 1

The correct option is C $204.8cm/s$

We can write two equations:

$l_1+e=\frac{v}{4f}$ and $l_2+e=\frac{3v}{4f}$

Now, $l_2-l_1=\frac{2v}{4f}=\frac{v}{2f}$

Differentiate, $\frac{△(l_2-l_1)}{l_2-l_1}=\frac{△v}{v}$

$△v=△(l_2-l_1)\frac{v}{l_2-l_1}=△(l_2-l_1)\left(2f\right)$

To maximize error,

$△v=(△l_1+△l_2)\left(2f\right)=2\times 512(0.1+0.1)=2\times 512\times 0.2=204.8cm/s$