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NEET PHYSICSMedium

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∘C27^\circ\text{C}, two successive resonances are produced at 20 cm20 \text{ cm} and 73 cm73 \text{ cm} column length. If the frequency of the tuning fork is 320 Hz320 \text{ Hz}, the velocity of sound in air at 27∘C27^\circ\text{C} is:

A

330 m/s330 \text{ m/s}

B

339 m/s339 \text{ m/s}

C

350 m/s350 \text{ m/s}

D

300 m/s300 \text{ m/s}

Step-by-Step Solution

Given: First resonance length, l1=20 cm=0.20 ml_1 = 20 \text{ cm} = 0.20 \text{ m} Second resonance length, l2=73 cm=0.73 ml_2 = 73 \text{ cm} = 0.73 \text{ m} Frequency of the tuning fork, f=320 Hzf = 320 \text{ Hz}

For a resonance tube (closed at one end), the distance between two successive resonance lengths is equal to half the wavelength (λ2\frac{\lambda}{2}): l2−l1=λ2l_2 - l_1 = \frac{\lambda}{2} λ=2(l2−l1)\lambda = 2(l_2 - l_1) λ=2(0.73−0.20)=2(0.53)=1.06 m\lambda = 2(0.73 - 0.20) = 2(0.53) = 1.06 \text{ m}

The velocity of sound vv is given by the relation v=fλv = f\lambda: v=320×1.06=339.2 m/sv = 320 \times 1.06 = 339.2 \text{ m/s} Rounding to the nearest given option, the velocity of sound is approximately 339 m/s339 \text{ m/s}.

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