Question

The speed of sound as measured by a student in the laboratory on a winter day is 340 m/s when the room temperature is 17 °C. What speed will be measured by another student repeating the experiment on a day when the room temperature is 32 °C?

Answer 1

Answer ⇒ 349 m/s.

Explanation ⇒ We know speed of the sound is directly proportional to the under root of the temperature.

Let the speed of the sound at 17 °C or 290 K be V.

When speed will become V', then let temperature be T' (32 + 273 = 305 K).

∴ V'/V = √(T'/T)

∴ V'/340 = √(305/290)

∴ V'/340 = 1.025

∴ V' = 348.7 m/s. ≈ 349 m/s.

Hence, the speed of the sound measured at 305 K or 32° C is 349 m/s.

Hope it helps.

Answer 2

Explanation:

It is given that,

Speed of sound, $v_1=340\ m/s$

Temperature, $T_1=17^{\circ} C=17+273=290\ K$

Temperature, $T_2=32^{\circ} C=32+273=305\ K$

We need to find the speed of sound when the room temperature is T₂. The speed of sound and temperature has the following relationship as :

$v\propto \sqrt{T}$

So, $\dfrac{v_1}{v_1}=\dfrac{\sqrt{T_1} }{\sqrt{T_2} }$

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

$\dfrac{340}{v_2}=0.975$

$v_2=348.71\ m/s$

or

$v_2=349\ m/s$

So, the speed of sound at 32 degrees Celsius is 349 m/s. Hence, this is the required solution.