A submarine Travels through water at a speed of `8.00(m)/(s)`, emitting a sonar wave at a frequency of 1400 Hz. The speed of sound in the water is 1533 m/s. What frequency is detected by an observer riding on another submarine moving with speed of `9.00(m)/(s)` as the submarines approach each other?

Explanation

Even through the problem involves subs moving in water, there is a Doppler effect just like there is when you are in a moving car and listening to sound moving through the air from another car. Because both subs are moving, we categorize this problem as one involving the Doppler effect for both a moving source and a moving observer. We can find the Doppler-shifted frequency heard by the observer in sub being careful with the signs of the source and observer velocities:
`f'=((v+v_0)/(v-v_S))f`
`=[(1533(m)/(s)+(+9.00(m)/(s)))/(1533(m)/(s)-(+8.00(m)/(s)))](1400Hz)=1416Hz`