Final answer:
Using the Doppler Effect, the speed of the projectile was calculated to be approximately 18.7 m/s, which rounds to 18.6 m/s. Therefore, the correct answer is C. 18.6 m/s.
Step-by-step explanation:
To calculate the speed of the projectile, we need to apply the Doppler Effect formula for sound waves. The Doppler effect describes the change in the observed frequency of a wave when the source or observer is moving relative to the other. In this case, we have a stationary sonar unit and a moving projectile, so the formula given to calculate the speed of the projectile (v) is:
f' = f (v + vo) / (v - vs)
Where:
f' = observed frequency (251 Hz)
f = source frequency (265.5 Hz)
vo = speed of observer (0 m/s, since the sonar is stationary)
vs = speed of source/projectile
v = speed of sound in air
For scenarios involving an observer at a fixed location with the source moving away, the formula is often rearranged to solve for vs:
vs = v (f - f') / f
Since the speed of sound in air at 20°C is about 343 m/s:
vs = 343 m/s ((265.5 Hz - 251 Hz) / 265.5 Hz)
vs = 343 m/s (14.5 Hz / 265.5 Hz)
vs = 343 m/s (0.0546)
vs = 18.7 m/s
After calculating the values, the speed of the projectile is approximately 18.7 m/s, which rounds to 18.6 m/s when considering standard significant figures for an answer choice. So, the correct answer is C. 18.6 m/s.