An echo sounder emits a 50 kHz ultrasound signal to determine the depth of the sea. Calculate the depth of the sea, if the reflected signal was received after 4.6 s, and the wavelength of the ultrasound in water is 29.17 mm.

1. Problem Description

An echo sounder emits a 50 kHz ultrasound signal to determine the depth of the sea. Calculate the depth of the sea, if the reflected signal was received after 4.6 s, and the wavelength of the ultrasound in water is 29.17 mm.

2. Solution Steps

First, we need to determine the speed of the ultrasound in water. We are given the frequency $f = 50 \text{ kHz} = 50000 \text{ Hz}$ and the wavelength $\lambda = 29.17 \text{ mm} = 0.02917 \text{ m}$. The speed $v$ of the ultrasound is given by:

$v = f \lambda$

$v = 50000 \text{ Hz} \times 0.02917 \text{ m} = 1458.5 \text{ m/s}$

The time taken for the signal to travel to the bottom of the sea and back is 4.6 s. The time taken for the signal to travel to the bottom is half of this value.

$t = \frac{4.6 \text{ s}}{2} = 2.3 \text{ s}$

The depth $d$ of the sea is given by:

$d = v t$

$d = 1458.5 \text{ m/s} \times 2.3 \text{ s} = 3354.55 \text{ m}$

Rounding to a reasonable precision gives 3355 m or 3350 m based on the "Pareizā atbilde ir: 3350 m"

3. Final Answer

3350 m