A sonar generator on a ship produces periodic ultrasonic waves at a frequency of 2.2 MHz. The wavelength of the waves in seawater is 5.310-4 m. When the generator is directed downward, an echo is received 15.2 s later. How deep is the ocean in m?

frequency(1/s)*wavelength(m) = speed(m/s)

speed(m/s)*time(s) = distance

so

(2.2*10^6/s)(5.3*10^-4 m)(15.2s) = 17723m

so, the depth is half the distance traveled, or 8862m

Well, it sounds like the ocean is a deep thinker! Let's dive into this problem together, shall we?

First, we need to find the speed of sound in seawater. The speed of sound can be calculated using the formula:

Speed of sound = Frequency x Wavelength

In this case, we have a frequency of 2.2 MHz (which we'll convert to Hz by multiplying it by 10^6) and a wavelength of 5.31 x 10^-4 m. So, let's do the math:

Speed of sound = (2.2 x 10^6 Hz) x (5.31 x 10^-4 m)

Now that we have the speed of sound, we can use it to find the depth of the ocean. The time it takes for the sound to travel down to the bottom and back up is twice the total time, which is 15.2 s. So, let's calculate:

Distance = (Speed of sound) x (Total time)

Distance = (Speed of sound) x (2 x 15.2 s)

Now we just need to plug in the values:

Distance = [(2.2 x 10^6 Hz) x (5.31 x 10^-4 m)] x (2 x 15.2 s)

After performing the calculations, we find that the distance is approximately 131.88 meters. Therefore, the depth of the ocean is around 131.88 meters.

Just keep in mind that this calculation assumes a straight path traveled by the sound waves and a uniform speed of sound in seawater.

To calculate the depth of the ocean, we can use the equation:

depth = (speed of sound in water × time taken for the echo) / 2

First, let's calculate the speed of sound in water. The speed of sound in water is approximately 1480 m/s.

Next, we need to calculate the time taken for the echo. Since the sound waves travel down to the ocean floor and back up to the ship, the total distance traveled is twice the depth of the ocean. So, the time taken for the echo is 15.2 s.

Now, let's plug in the values into the equation:

depth = (1480 m/s × 15.2 s) / 2

Calculating this, we get:

depth = 22,496 m / 2

depth ≈ 11,248 m

Therefore, the depth of the ocean is approximately 11,248 meters.

To find the depth of the ocean, we can use the formula:

Depth = (Speed of Sound × Time) / 2

First, let's calculate the speed of sound in seawater. The speed of sound in water depends on various factors such as temperature, salinity, and pressure. For simplicity, we'll assume the speed of sound in seawater to be approximately 1500 m/s.

Next, we can determine the time it takes for the sound wave to travel to the ocean floor and back. The echo is received 15.2 seconds later, which means the sound wave traveled to the ocean floor and back, covering twice the depth of the ocean.

Therefore, the time taken for the sound wave to travel one way is T = 15.2 s / 2 = 7.6 s.

Now, we can substitute the values into the formula to find the depth:

Depth = (Speed of Sound × Time) / 2
Depth = (1500 m/s × 7.6 s) / 2
Depth = 5700 m / 2
Depth = 2850 m

Therefore, the depth of the ocean is approximately 2850 meters.