Fishing sonar. The attenuation constant for sound waves in water increases with frequency. Consider the sonar used for fishing. The reflection of sound from fish schools is used for sports and commercial fishing. Fish produce relatively large reflections because of their air sack, the reflection being due to the interface between flesh and air, whereas the reflection at the interface between flesh and water is small. The signal is generated by an ultrasound actuator and detected by an ultrasound sensor. Suppose the actuator produces a power of 0.1 W at 50 kHz (a common frequency in fishing sonars) and the power propagates in a relatively narrow beam. Assuming that 20% of the sound reaching a fish school is reflected and that reflected sound is scattered uniformly over a half-sphere, calculate the required sensitivity of the ultrasonic sensor (in W/m2 ) to detect a fish school at a depth of 20 m. Attenuation in water at 50 kHz is 15 dB/km.