On a winter day, a student in the laboratory measures the speed of sound to be 340 m s^ -1 when the room temperature is 17^ ^ ^ C . Determine the speed that will be measured by another student performing the same

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 349 m s^ -1

The speed of sound in a gas is directly proportional to the square root of its absolute temperature,

v \propto \sqrt{T}

.

Given

v_1 = 340 \text{ m s}^{-1}

at

T_1 = 17^{}^{{}^{\circ}} \text{C} = 17 + 273 = 290 \text{ K}

.

We need to find the speed

v_2

at

T_2 = 32^{}^{{}^{\circ}} \text{C} = 32 + 273 = 305 \text{ K}

.

Using the relation

\dfrac{v_2}{v_1} = \sqrt{\dfrac{T_2}{T_1}}

:

v_2 = 340 \sqrt{\dfrac{305}{290}}

v_2 = 340 \sqrt{\dfrac{61}{58}}

v_2 \approx 340 \times 1.0255 \approx 348.7 \text{ m s}^{-1}

Rounding to the nearest integer gives

349 \text{ m s}^{-1}

.

On a winter day, a student in the laboratory measures the speed of...

Options

Correct answer

Step-by-step solution

More from Sound Waves