Answer:
A) 2 possible frequencies of second propellar = 424 rpm or 724 rpm
B) Correct frequency is f2 = 724 rpm
C) Reason is stated in explanation
Explanation:
A) We are given;
Frequency of first propeller; f1 = 574 rpm
Beat frequency; f_beat = 2.5 Hz = 2.5 × 60 rpm = 150 rpm
Now, formula for the beat frequency is;
f_beat = |f1 - f2|
Now, |f1 - f2| means it is inside an absolute value.
Thus, it means,
f1 - f2 = 150 or f2 - f1 = 150
Thus;
574 - f2 = 150
Or f2 - 574 = 150
So,f2 = 574 - 150 = 424 rpm or f2 = 574 + 150 = 724 rpm
2 possible frequencies of second propellar = 424 rpm or 724 rpm
B) Now, if we increase the speed of the second propellar slightly, it means that f2 will increase as well.
Now, from the 2 possible values of f2 gotten, we can see that for f1 - f2 = 150, when we increase f2, the beat frequency will reduce while for f2 - f1 = 150, when we increase f2, the beat frequency will increase.
Thus, it's the frequency of f2 gotten in f2 - f1 = 150 that is the correct answer.
Thus, when we increase the speed of the second propellar slightly, it means that;
f2 = 724 rpm
C) Answer in part B is correct because as we increase the speed of the second propellar, the frequency will also increase and the value of f2 that corresponds with an increase in speed is 724 rpm.
