Yes, a high-pitched sound emitted from a depth of 13,000 feet in the ocean would sound deeper when heard on the surface. This is due to the way sound waves travel through water.
Sound travels faster in water than in air, with an approximate speed of about 1,500 meters per second (or about 4,921 feet per second) in seawater. As sound waves propagate through the water, they can be affected by factors such as temperature, pressure, and salinity.
When a high-pitched sound is emitted at a depth of 13,000 feet, it will undergo dispersion and attenuation as it travels to the surface. Dispersion refers to the spreading out of different frequencies within the sound wave, while attenuation refers to the gradual decrease in sound intensity with distance.
As the sound wave travels upward, the dispersion and attenuation processes cause the higher frequencies to be attenuated more than the lower frequencies. This phenomenon is known as frequency-dependent absorption.
Therefore, when the sound wave reaches the surface and is heard by someone, the higher frequencies will have been more significantly absorbed or attenuated during the journey. As a result, the sound will be perceived as deeper or lower in pitch compared to its original high-pitched emission.
In summary, due to the properties of sound propagation in water, a high-pitched sound emitted from a great depth in the ocean would indeed sound deeper on the surface when heard by a person.