Question

find temperature at which velocity of sound in air is two times its velocity at 10°C (take speed of sound at 10°C is 338m/s)​

Answer 1

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Answer 2

SOLUTION

TO DETERMINE

The temperature at which velocity of sound in air is two times its velocity at 10°C (take speed of sound at 10°C is 338m/s)

EVALUATION

We know that

$\sf{v(t) = 332 + 0.6t \: \: \: - - - (1)}$

Here it is given that speed of sound at 10°C is 338m/s

Thus we have v(10) = 338

So we get

$\sf{v(10) = v(0) +( 0.6 \times 10)}$

$\sf{ \implies \: 338 = v(0) +6}$

$\sf{ \implies \: v(0) = 332}$

Let the required temperature = t°C

So we have v(t) = ( 2 × 338 )

Which gives v(t) = 676

From Equation 1 we get

$\sf{676= 332 + 0.6t }$

$\sf{ \implies \: 676 - 332 = 0.6t }$

$\sf{ \implies \: 0.6t = 344 }$

$\sf{ \implies \: t = 573.33 }$

FINAL ANSWER

Hence the required temperature = 573.33°C

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