What happens to the sound waves at point C ? The frequency of the sound waves is 20 kHz . If the speed of the sound in water is $$ 1500 \mathrm{~m} \cdot \mathrm{~s}^{-1} $$, calculate the wavelength of the sound waves in water. Calculate the depth of the water beneath the ship, If the waves take 8,5 seconds to move from A to B .

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To solve the problem, we will follow these steps:

1. **Calculate the wavelength of the sound waves in water.**
2. **Calculate the depth of the water beneath the ship using the time taken for the sound waves to travel from point A to point B.**

### Step 1: Calculate the Wavelength

The wavelength $$\lambda$$ of a sound wave can be calculated using the formula:

$$
\lambda = \frac{v}{f}
$$

where:
- $$v$$ is the speed of sound in water ($$1500 \, \text{m/s}$$),
- $$f$$ is the frequency of the sound waves ($$20 \, \text{kHz} = 20000 \, \text{Hz}$$).

Now, let's calculate the wavelength.

### Step 2: Calculate the Depth of Water

The depth $$d$$ can be calculated using the formula:

$$
d = \frac{v \cdot t}{2}
$$

where:
- $$t$$ is the time taken for the sound waves to travel from A to B ($$8.5 \, \text{s}$$).
- The factor of 2 is used because the sound wave travels to the bottom and back up.

Now, let's perform the calculations.

First, we will calculate the wavelength, and then we will calculate the depth.

Let's proceed with the calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1500}{20000}$$
- step1: Reduce the fraction:
  $$\frac{3}{40}$$
Calculate or simplify the expression $$ 1500 * 8.5 / 2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1500\times 8.5}{2}$$
- step1: Multiply the numbers:
  $$\frac{12750}{2}$$
- step2: Reduce the fraction:
  $$6375$$
### Results of the Calculations

1. **Wavelength Calculation:**
   The wavelength $$\lambda$$ of the sound waves in water is:
   $$
   \lambda = 0.075 \, \text{m}
   $$

2. **Depth Calculation:**
   The depth $$d$$ of the water beneath the ship is:
   $$
   d = 6375 \, \text{m}
   $$

### Summary
- The wavelength of the sound waves in water is $$0.075 \, \text{m}$$.
- The depth of the water beneath the ship is $$6375 \, \text{m}$$.

If you have any further questions or need additional calculations, feel free to ask!
The wavelength of the sound waves in water is 0.075 meters, and the depth of the water beneath the ship is 6375 meters.

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