You are on a tugboat in heavy fog and the crew knows that there is a long cliff band on shore that they are very nervous about hitting. Having just finished your physics class you realize that you could build an early warning system with an old guitar and an LRC circuit that are in the ships work room. You will use the foghorn sound wave bouncing off the cliffs to trigger an LRC circuit attached to a guitar pickup.
The foghorn is emitting blasts with a wavelength of 9 meters. A quick calculation tells you that the intensity will be just big enough when the tugboat is about 1/4 mile from shore. Just enough time to stop the tugboat from hitting the cliffs. You want to tune the LRC circuit to have the maximum sensitivity to the foghorn sound bouncing off the cliffs.
If it is 4 degrees Celsius outside and the tugboat is moving toward the cliffs at 24.4 m/s and you have an LRC circuit with a 12.5 micro Henry inductor what should you set the variable capacitance capacitor at (in Farads) to get the best signal? Assume you are traveling straight at the cliffs and that you can tune the strings of the guitar to best match the frequency of the waves coming back from the cliffs. Also, assume that the air is dry for any calculations that would change with humidity. Please round your answer to two decimal places.