Question

The speed of sound of a wave of frequency 200Hz in the air is 340m/s. The speed of sound of the wave of frequency 400 Hz in the same air is ?​

Answer 1

Answer:

V2 = 680 m/s

Explanation:

$\sf We\: know\: that\: , \\ \\ \sf frequency \alpha speed \\ \\ \sf f \alpha v \\ \\ \sf {f}_{1} = 200 Hz \: \: \: {f}_{2} = 400 Hz \\ \sf {V}_{1} = 340 m{s}^{-1} \: \: {V}_{2} = ? \\ \\ \sf \frac{{f}_{1}}{{f}_{2}} = \frac {{V}_{1}}{{V}_{2}} \\ \\ \sf \frac{200}{400} = \frac{340}{{V}_{2}} \\ \\ \sf \frac{1}{2}= \frac{340}{{V}_{2}} \\ \\ \sf {V}_{2} = 340 × 2 \\ \\ \sf {V}_{2} = 680 m{s}^{-1} \\ \\ \boxed { \bold{\red{ \sf {V}_{2} = 680 m{s}^{-1}}}}$

Answer 2

Answer:

The speed of sound of the wave of frequency 400 Hz in the same air is 340 m/s.

Explanation:

Assumption,

Let the speed of sound of the wave of frequency (f₂ = 400 Hz) in the air is (v₂).

Given,

The speed of sound of the wave with frequency (f₁ = 200 Hz) in the air is (v₁) = 340 m/s.

To find,

The speed of sound of the wave of frequency (f₂ = 400 Hz) in the air is (v₂).

Calculation,

The frequency of a sound indicates how fast the sound wave vibrates. This is independent of how fast the sound wave propagates. The higher the frequency, the faster the pressure of the sound wave changes and the shorter the wavelength.

The sound wave propagation depends on the energy of the molecules in the transmission medium  (temperature), the spatial proximity of the molecules  (density), the mass of the molecules, and their phase (gaseous, liquid, solid), and structure.

Sound generally travels faster in solids because the molecules are closer together, so the molecules have a shorter distance to transmit the sound wave to the next molecule. Conversely, they generally move more slowly in gas because the molecules have to travel farther before they can transfer sound energy to the next molecule.

Therefore, If the frequency gets increased from 200 Hz to 400 Hz, then the wavelength of the sound decreases accordingly keeping the speed of sound in the air constant.

Therefore, the speed of sound of the wave of frequency 400 Hz in the same air is 340 m/s.

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