Question

A tuning fork was sounded over the open end of an air column, and produced $4$ beats/ sec when temperature of air was ${20}^{\circ }C$. The tuning fork gave the lower note when the temperature gradually decreased to $5^{\circ }C$, the tuning fork produced $3$ beats per second. The frequency of the tuning fork is (in $Hz)$.

• A. $27$
• B. $14$
• C. $34$
• D. $63$

Answer 1

The correct option is B $14$

Let v be frequency of tunning fork

At $t=20°C,T=273+20=293K$

$n=v+4$

At $t=5°C,T=273.5=278K$

$n=v+3$

Now $n\alpha T\therefore \frac{v+4}{v+3}=\frac{293}{278}\Rightarrow 15v=(278\times 4)-(293\times 3)\Rightarrow 15v=233\Rightarrow v\approx 14Hz$