Explanation:

The given figure shows a tuning fork of frequency 700 Hz vibrating at one side of a tube. We need to find the velocity of sound if no sound is heard at the outer end.

Resonance:

When a tuning fork of a certain frequency is brought close to an open tube, the air column inside the tube starts vibrating at the same frequency as that of the fork. This is known as resonance. The length of the air column inside the tube can be adjusted to produce resonance at a particular frequency.

Conditions for resonance:

For resonance to occur, the following conditions must be met:

- The frequency of the sound wave produced by the tuning fork must be equal to the natural frequency of the air column inside the tube.
- The length of the air column inside the tube must be a multiple of half-wavelength.

Velocity of sound:

The velocity of sound in air is given by the formula:

v = fλ

where v is the velocity of sound, f is the frequency of the sound wave, and λ is the wavelength of the sound wave.

Calculation:

In the given figure, the tuning fork is vibrating at a frequency of 700 Hz. Let the length of the air column inside the tube be L.

- At resonance, the length of the air column inside the tube is equal to half-wavelength.

L = λ/2

- Substituting the value of λ in the formula for velocity of sound, we get:

v = fλ = 2fL = 2 x 700 x 0.35 = 490 m/s

Therefore, the velocity of sound is 490 m/s.

Conclusion:

In conclusion, the velocity of sound in air is 490 m/s when a tuning fork of frequency 700 Hz is vibrating at one side of a tube and no sound is heard at the outer end.

If there is no sound then there r no beats hence frequency of vibrating air column must be 700 Hz According to the given over tone and length of tube it decides velocity of sound