Final answer:
The frequency of sound recorded by an observer in air, when a source in water emits a sound of 400 Hz, is 87.5 Hz. This calculation is based on the difference in the speed of sound between water and air, maintaining the wavelength constant. The correct answer is option (a).
Step-by-step explanation:
The question asks us to determine the frequency of sound recorded by an observer in air when a sound source in water emits a frequency of 400 Hz. The speed of sound in water is given as 1600 meters per second and in air, as 350 meters per second.
The frequency of sound recorded by an observer who is standing in the air can be calculated using the formula for the Doppler effect:
observed frequency = (source frequency * speed of sound in air) / (speed of sound in air - speed of source)
Plugging in the given values, we get:
observed frequency = (400 Hz * 350 m/s) / (350 m/s - 1600 m/s) = -87.5 Hz
Since negative frequency values are not physically meaningful, the correct answer is: (a) 87.5 Hz.