Question

1) Find the speed of sound in air at 50 °C and 70°C (take speed of sound 332 mis), is im hle
$332 \times \sqrt{323 \div 273}$
​

Answer 1

Answer:

TO DETERMINE

The speed of sound in air at 50°C and 70°C (take speed of sound 332m/s)

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

\sf{v(t) = v(0) + 0.6t}v(t)=v(0)+0.6t

Where v(t) = Velocity of sound at t°C

v(0) = Velocity of sound at 0°C

EVALUATION

We know that

\sf{v(t) = v(0) + 0.6t}v(t)=v(0)+0.6t

Here it is given that speed of sound 332m/s

∴ v(0) = 332

So above equation reduces to

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

Speed at 50°C

∴ t = 50

\sf{v(50) = 332 + 0.6 \times 50 }v(50)=332+0.6×50

\sf{ \implies \: v(50) = 332 + 30 }⟹v(50)=332+30

\sf{ \implies \: v(50) = 362}⟹v(50)=362

So speed of sound at 50°C is 362 m/s

Speed at 70°C

∴ t = 70

\sf{v(70) = 332 + 0.6 \times 70 }v(70)=332+0.6×70

\sf{ \implies \: v(70) = 332 + 42 }⟹v(70)=332+42

\sf{ \implies \: v(70) = 374 }⟹v(70)=374

So speed of sound at 70°C is 374 m/s

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