Answer :
Final answer:
To determine how far a deep-sea diver should be to hear an echo, one must consider the time for the sound to travel to and from the rock. For an echo returning in one second, the diver would need to be 750 meters away, assuming a sound speed of 1500 m/s. The provided answer choices do not match this scenario, but the calculation method is the same as that used in sonar technology and oceanography for depth measurement.
Explanation:
To calculate how far from an undersea rock a deep-sea diver should be to hear his own echo with a sound speed of 1500 meters per second, one needs to consider the time it takes for sound to travel to the rock and back. Since the initial question does not provide a time, let's use a method similar to how depth is determined in oceanography and sonar technology.
In oceanography, an echosounder is used for mapping bathymetry by sending out a pulse and timing the echo. The depth is half the product of the speed of sound in water and the time it takes for an echo to return. If a diver wants to hear an echo, the same principle applies.
The time taken, in this case, is the round trip time which is twice the distance divided by speed. We do not know the exact time it takes for the echo to return to the diver, but for simplicity, let's calculate for a one-second round trip time. If we have an echo returning in one second, it would mean the sound has traveled for half a second to reach the rock and then half a second to return.
For the diver to hear their own echo, they should be at least 750 meters away from the rock, which is half the distance sound travels in one second; so none of the provided options (a, b, c, d) are correct given a time of 1 second for the sound to return. If, however, we choose a different round-trip time conforming to the options provided, the process would be to divide the time of the echo by two, multiply by the speed of sound, and that would give the one-way distance to the object creating the echo.
