How can the depth Z be determined using sound instead of physical measures?

To determine depth using sound, the correct method involves sending a sound wave to the seabed and measuring the time it takes for the wave to return. This technique is known as sonar, which stands for Sound Navigation and Ranging. When the sound wave travels to the seabed and is reflected back, the time it takes for the round trip can be used to calculate the depth.

The speed of sound in water is relatively constant, typically around 1500 meters per second, so by multiplying the time it takes for the echo to return by the speed of sound and then dividing by two (since the sound wave travels to the seabed and back), you can accurately determine the depth.

Using sound instead of physical measures is advantageous in hydrographic surveying because it allows for measurements across large areas quickly and efficiently without needing to physically touch the seabed. This method is particularly useful in deep or inaccessible waters where direct measurements would be impractical or impossible.

In contrast, the other methods suggested either do not utilize sound effectively, or rely on direct physical interaction with the seabed, which may not be feasible in many scenarios encountered in hydrographic surveys.