Question

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

• A. 300 m/s
• B. 330 m/s
• C. 350 m/s
• D. 339 m/s

Answer 1

The Correct Option is D

To solve this problem, we need to determine the speed of sound in air based on the information provided about resonance in the glass tube. We know the conditions that two successive resonances occur at an air column length of 20\, \text{cm} and 73\, \text{cm}. We also know the frequency of the tuning fork is 320\, \text{Hz}.

In resonance problems involving a closed tube (open at one end), the condition for successive resonances happens at intervals corresponding to changes in the length of a half wavelength of sound in the air. Let's explore the steps to calculate the speed of sound:

1. In open tube resonance, the difference in length between two successive resonances is equal to half the wavelength (\frac{\lambda}{2}) of the sound. Here, the change in length is 73\, \text{cm} - 20\, \text{cm} = 53\, \text{cm} = 0.53\, \text{m}.
2. This change corresponds to half the wavelength. Thus, \frac{\lambda}{2} = 0.53\, \text{m}, giving \lambda = 2 \times 0.53\, \text{m} = 1.06\, \text{m}.
3. The speed of sound is given by the formula v = f \times \lambda, where f is the frequency.
4. Substituting the given values, v = 320\, \text{Hz} \times 1.06\, \text{m} = 339.2\, \text{m/s}.

Therefore, the calculated velocity of sound in air at 27^{\circ}\text{C} is approximately 339\, \text{m/s}.

This matches the correct answer given in the options.