The sonar of a stationary ship sends a signal with a frequency of 5.0x103-Hz through water. If the signals speed is 1.5x103-m/s and the echoes detection is 3.9-sec later. What is the depth of the water under the ship?
Well, to calculate the depth of the water, we need to consider a few things. First of all, I must say, the water is deep, so deep that it's probably homes to some mysterious sea creatures and sunken ships!
Now, let's calculate the depth. We know that the sonar sends a signal into the water, and it takes 3.9 seconds for the echo to return. Speed is equal to distance divided by time, so we can use this formula to find the distance traveled by the signal.
The speed of sound in water is 1.5x10^3 m/s, and the echo takes 3.9 seconds. So we can use the formula distance = speed x time.
Distance = 1.5x10^3 m/s x 3.9 s = 5.85x10^3 meters.
Therefore, the depth of the water under the ship is approximately 5.85 kilometers. Imagine all the fish swimming around down there!
To find the depth of the water under the ship, we need to determine the round trip time for the sonar signal.
1. Since the signal travels to the bottom and back, the round trip time is twice the detection time: 2 * 3.9 sec = 7.8 sec.
2. We can use the formula v = d/t, where v is the speed of the signal, d is the distance traveled, and t is the time taken.
3. Rearranging the formula to solve for the distance, d = v * t.
4. Plug in the values: d = (1.5x10^3 m/s) * 7.8 sec.
5. Multiply the speed and time: d = 11.7x10^3 meters.
Therefore, the depth of the water under the ship is approximately 11.7 kilometers.
To find the depth of the water under the ship, we can use the equation:
depth = (speed of sound in water * time) / 2
First, let's find the speed at which the sonar signal travels through water. The speed of sound in water is given as 1.5 x 10^3 m/s.
Next, calculate the time it takes for the echo to be detected. In this case, the time is given as 3.9 seconds.
Now, we can substitute the values into the equation:
depth = (1.5 x 10^3 m/s * 3.9 s) / 2
Calculating this equation will give us the depth of the water under the ship.
d = V*t = 1500m/s * 3.9s = 5850 m.=Total
distance traveled.
Depth = 5850/2 = 2925 m.