What time is required for sound to travel 5km if the tempreture is 15 degree centigrate?
14.7m/s
first, find the velocity of sound at that temperature.
vs=331.4+15*0.6 =340
time=distance/velocity=5000/340=14.7 seconds
To determine the time required for sound to travel 5km at a specific temperature, we need to consider the speed of sound in air. The speed of sound varies with temperature. The relationship between temperature and the speed of sound in air is given by the formula:
v = 331.5 + 0.6 * T
Where:
v is the speed of sound in meters per second (m/s)
T is the temperature in degrees Celsius (°C)
To calculate the time required, we need to find the speed of sound at the given temperature (15°C), convert the distance to meters, and then divide the distance by the speed of sound.
Step 1: Calculate the speed of sound at 15°C
Using the formula, substitute T = 15 into the equation:
v = 331.5 + 0.6 * 15
v = 331.5 + 9
v ≈ 340.5 m/s
Step 2: Convert the distance to meters
5 km is equal to 5,000 meters.
Step 3: Calculate the time required
Time = Distance / Speed
Time = 5,000m / 340.5 m/s
Time ≈ 14.68 seconds
Therefore, it would take approximately 14.68 seconds for sound to travel 5 km at a temperature of 15°C.