A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be a

Question

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27^\circ	ext{C}$, two successive resonances are produced at $20 	ext{ cm}$ and $73 	ext{ cm}$ column length. If the frequency of the tuning fork is $320 	ext{ Hz}$, the velocity of sound in air at $27^\circ	ext{C}$ is:

Accepted Answer

Given:
First resonance length, $l_1 = 20 	ext{ cm} = 0.20 	ext{ m}$
Second resonance length, $l_2 = 73 	ext{ cm} = 0.73 	ext{ m}$
Frequency of the tuning fork, $f = 320 	ext{ Hz}$

For a resonance tube (closed at one end), the distance between two successive resonance lengths is equal to half the wavelength ($\frac{\lambda}{2}$):
$$l_2 - l_1 = \frac{\lambda}{2}$$
$$\lambda = 2(l_2 - l_1)$$
$$\lambda = 2(0.73 - 0.20) = 2(0.53) = 1.06 	ext{ m}$$

The velocity of sound $v$ is given by the relation $v = f\lambda$:
$$v = 320 	imes 1.06 = 339.2 	ext{ m/s}$$
Rounding to the nearest given option, the velocity of sound is approximately $339 	ext{ m/s}$.

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