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°C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is

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

Answer 1

The Correct Option is C

The question requires determining the velocity of sound in air given specific conditions of resonance frequencies and lengths in a glass tube. To solve this, we utilize the concept of resonance in air columns.

**Concept:**

When a tuning fork is used to produce resonance in an open or closed tube, standing waves are established in the tube. The positions of resonance are where the lengths of the air column provide standing waves longer by a half-wavelength.

Given:

• Two successive resonances occur at 20 cm and 73 cm lengths.
• Frequency of the tuning fork \nu = 320 \, \text{Hz}

**Method:**

For successive resonances in a closed tube (first resonance and a successive one), the difference in the lengths of air column corresponds to half the wavelength of the sound.

Therefore, the difference in length between the two successive resonances is:

\Delta L = L_2 - L_1 = 73 \, \text{cm} - 20 \, \text{cm} = 53 \, \text{cm} = 0.53 \, \text{m}

This difference represents half the wavelength of the sound. Thus, \Delta L = \frac{\lambda}{2}

\lambda = 2 \times \Delta L = 2 \times 0.53 \, \text{m} = 1.06 \, \text{m}

Using the formula for wave speed, v = \nu \lambda, we calculate the velocity of sound.

Substitute the known values:

v = 320 \, \text{Hz} \times 1.06 \, \text{m}

v = 339.2 \, \text{m/s}

Considering significant figures, the velocity of sound at 27°C is approximately 339 m/s.

Hence, the correct answer is 339 m/s.