An explosion occurs at an altitude of 312 m above the ground. If the air temperature is -10.00°C, how long does it take the sound to reach the ground?
[velocity of sound at \(0^oC\) = 331 ms-1]
0.94s
0.96s
0.93s
0.95s
Explanation
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To solve this problem, we need to calculate the time it takes for sound to travel 312 m to the ground at the given temperature of -10.00°C.
Step 1: Determine the velocity of sound
The speed of sound in air changes with temperature according to the formula:
V = Vo √1 + T/273.15
Vo = 331 m/s (speed of sound at 0°C)
T = -10.00°C
Substitute the values:
V = 331 √ 1 + (-10/273.15)
V = 331 × √0.9634
V = 324.88 m/s
Step 2: Calculate the time
The time (t) it takes for sound to travel a distance (d) is given by:
t = d/v
Substitute the values:
t = 312/324.88
t = 0.96 sec
Thrrefore, The time it takes for the sound to reach the ground is approximately 0.96 s.
Correct Option: B. 0.96 s
To find the time it takes for the sound to reach the ground, we first need to calculate the speed of sound at the given temperature.
v = v0 + (0.6 * T)
where v0 is the speed of sound at 0°C (331 m/s)
T is the temperature in °C.
v = 331 + (0.6 * -10)
v = 331 - 6
v = 325 m/s
Calculate Time
Time = Distance / Speed
Time = 312 m / 325 m/s
Time ≈ 0.96 s
Correct Option is B.
