A ship is anchored in a bay. The echo of the ship's foghorn, reflected from an iceberg, is heard 5.0 seconds after the horn is sounded. The temperature of the air is -10.0 degrees Celsius. How many meters away is the iceberg? Show your work.
Vs = 332 + 0.6*(-10) = 326 m/s = Velocity of sound.
d = Vs * t/2 = 326 * 5/2 = 815 m.
To calculate the distance to the iceberg, we need to use the speed of sound in air and the time it takes for the sound to travel from the ship to the iceberg and back (round trip).
1. First, let's calculate the speed of sound in air. The speed of sound in air can be approximated using the formula:
speed of sound = 331.4 + (0.6 x temperature in degrees Celsius)
Plugging in the temperature of -10.0 degrees Celsius:
speed of sound = 331.4 + (0.6 x -10.0)
= 331.4 - 6.0
= 325.4 meters per second
2. Since the sound travels from the ship to the iceberg and back, we need to divide the time by 2 to get the one-way time. So, the time for the sound to travel from the ship to the iceberg is 5.0 seconds / 2, which is 2.5 seconds.
3. Now, we can calculate the distance to the iceberg. Using the formula:
distance = speed x time
Plugging in the values:
distance = 325.4 meters per second x 2.5 seconds
= 813.5 meters
Therefore, the iceberg is approximately 813.5 meters away from the ship.
To find the distance to the iceberg, we can use the speed of sound in air and the time it takes for the echo to reach the ship.
Step 1: Find the speed of sound in air.
The speed of sound in air depends on the temperature of the air. The formula to calculate the speed of sound in air is:
v = 331.4 + 0.6 * T
where v is the speed of sound in meters per second and T is the temperature in degrees Celsius.
Plugging in the temperature of the air (-10.0 degrees Celsius), we can calculate the speed of sound in air as:
v = 331.4 + 0.6 * (-10.0) = 331.4 - 6 = 325.4 m/s
Step 2: Calculate the distance to the iceberg.
The time it takes for the sound to travel to the iceberg and back is twice the time it takes for the echo to reach the ship. So, the time for the sound to reach the iceberg is half of the 5.0-second delay:
t = 5.0 / 2 = 2.5 seconds
The distance to the iceberg can be calculated using the formula:
distance = speed * time
Plugging in the calculated speed of sound in air (325.4 m/s) and the time (2.5 seconds), the distance to the iceberg is:
distance = 325.4 * 2.5 = 813.5 meters
Therefore, the iceberg is approximately 813.5 meters away from the ship.