An explosion occurs at an altitude of 312 m above the ground. If the air temperature is -10.00°C, how long…

1. Analyze the Question

We are given the altitude ($h = 312\text{ m}$) and the temperature ($T = -10.00^\circ\text{C}$). We need to find the time ($t$) it takes for the sound to travel to the ground. To do this, we must first determine the velocity of sound at the given temperature.

2. Explain the Concept

The velocity of sound in air is dependent on temperature. The relationship is given by the formula:

Where:

• $v_t$ = velocity at temperature $T$
• $v_0$ = velocity at $0^\circ\text{C}$ ($331\text{ m/s}$)
• $T_k$ = absolute temperature in Kelvin ($T^\circ\text{C} + 273$)
• $T_0$ = absolute temperature at $0^\circ\text{C}$ ($273\text{ K}$)

Alternatively, for small temperature changes, we use the approximation: $v_t \approx v_0 + 0.6T$. However, using the absolute temperature formula is more precise for physics examinations.

3. Show the Solution

Step 1: Convert temperature to Kelvin $T_k = -10 + 273 = 263\text{ K}$

Step 2: Calculate the velocity of sound at $-10^\circ\text{C}$

Step 3: Calculate the time taken Using the formula $t = \frac{\text{distance}}{\text{velocity}}$:

Rounding to two decimal places, we get 0.96s.

4. Identify the Answer

Comparing our result to the options provided: A. 0.94s B. 0.96s C. 0.93s D. 0.95s

The calculated value matches option B.

5. Exam Tip

When dealing with sound velocity and temperature in JAMB, always remember that sound travels slower in colder air. If your calculated velocity is higher than $331\text{ m/s}$ when the temperature is below $0^\circ\text{C}$, you know you have made a calculation error!