Final answer:
The correct time an ultrasonic transducer should record for a 1.00 mm thick nonstick-coated frying pan is approximately 1.05 µs. For the radar-invisible coating on an aircraft to inhibit 4.00-cm wavelength radar reflection, it should be about 8.33 mm thick, though this approach has practical limitations and may not be effective for all radar frequencies.
Step-by-step explanation:
To determine the minimum thickness of a coating on a frying pan using a nondestructive method, an ultrasonic transducer is used. The speed of the ultrasonic wave in the coating can be calculated using the formula speed (v) = frequency (f) × wavelength (λ). With the given frequency of 25 kHz and the wavelength of 0.076 m, the speed of the wave is v = 25,000 Hz × 0.076 m = 1,900 m/s. The time (t) it takes for the sound to travel through the coating twice (down and back) is calculated by t = 2d/v, where d is the coating thickness (1.00 mm or 0.001 m). Hence, t = (2 × 0.001 m) / 1,900 m/s ≈ 0.00105 seconds, or 1.05 µs. This is the time that should be recorded if the coating is the correct thickness.
Regarding the coating for making military aircraft invisible to radar, the quarter-wavelength rule tells us that to minimize reflection, the coating should be an odd-number multiples of a quarter of the radar's wavelength in the material. For a 4.00-cm (0.040 m) wavelength radar and a coating with an index of refraction of 1.20, the wavelength in the material is λ' = λ / n, so λ' = 0.040 m / 1.20 ≈ 0.0333 m. Therefore, the coating should be λ'/4, which is 0.0333 m / 4 ≈ 0.00833 m (8.33 mm) thick. One assumption that seems unreasonable is the practicality of coating an actual aircraft with such a precise thickness of material. It's also questionable whether such a simple approach would be effective against various radar frequencies.