A tuning fork with frequency $800\text{ Hz}$ produces resonance in a resonance column tube with upper end…
A tuning fork with frequency $800\text{ Hz}$ produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonance are observed at length $9.75\text{ cm}$, $31.25\text{ cm}$ and $52.75\text{ cm}$. The speed of sound in air is [NEET 2019]
500 ms$^{-1}$
156 ms$^{-1}$
344 ms$^{-1}$
172 ms$^{-1}$
Solution
For vibrating tuning fork over a resonance tube, the first resonance is obtained at the length
The diagram shows a resonance tube with water at the bottom, an antinode $A$ at the top, a node $N$ at the water surface, and length $l_1 = \lambda/4$.
$l_1 = \frac{\lambda}{4}$ ...(i)
For second resonance,
The diagram shows a longer resonance tube with an antinode $A$ at the top, a node $N$ in between, and total length $l_2 = \lambda/4 + \lambda/2$.