The speed of sound in air at 0°C is 332 m s⁻¹. What will be the speed of sound at 22 C? (345.2 m s⁻¹)


Given:

Initial Temperature = `\T_0` = 0°C = 273 K
Initial Speed of sound = `\v_0` = 332 m s⁻¹
Final Temperature = T = 22°C = 295 K

To Find:

Final Speed of sound  = v = ?

Solution:

Since

`\frac{v}{v_0}` = `\sqrt frac {T}{T_0}`

or

v = `\v_0` `\sqrt frac {T}{T_0}`

putting values

v = 332 m s⁻¹ `\sqrt frac {295 K}{273 K}`

v = 332 m s⁻¹ `\sqrt {1.081}`

v = 332 m s⁻¹ 𝐱 1.039

v = 345.1 m s⁻¹ ---------------Ans.


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