The velocity of sound in air at 15°C is 340ms\(^{-1}\). Calculate the velocity at 47\(^o\)C

The velocity of sound in air at 15°C is 340ms\(^{-1}\). Calculate the velocity at 47\(^o\)C

Given the velocity of sound at \( 15^\circ C \):

\(v_0 = 340 \, \text{m/s}\)

The absolute temperatures are:

\(T_0 = 15 + 273.15 = 288.15 \, \text{K}\)

\(T = 47 + 273.15 = 320.15 \, \text{K}\)

We use the formula for the velocity of sound:

\(v = v_0 \sqrt{\frac{T}{T_0}}\)

Substituting the known values:

\(v = 340 \times \sqrt{\frac{320.15}{288.15}}\)

Calculating the ratio of temperatures:

\(\frac{320.15}{288.15} \approx 1.111\)

Taking the square root:

\(\sqrt{1.111} \approx 1.054\)

Finally, calculating the new velocity:

\(v \approx 340 \, \text{m/s} \times 1.054 \approx 358.6 \, \text{m/s}\)

The velocity of sound in air at \( 47^\circ C \) is approximately:

\(v \approx 358.6 \, \text{m/s}\)

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