Sound

Step 1: Understanding the Concept
Beat frequency is the absolute difference between the frequencies of two sounding sources: . Harmonic frequencies are integer multiples of the fundamental frequency ( harmonic = ).

Step 2: Key Formula or Approach
1. .
2. .

Step 3: Detailed Explanation
1. From the first condition, can be either: - Hz - Hz
2. Now, test both possibilities with the second condition ( harmonic produces 10 beats with 420 Hz): - If Hz: Hz. Beat frequency with 420 Hz = Hz. (Matches given condition) - If Hz: Hz. Beat frequency with 420 Hz = Hz. (Does not match)

Step 4: Final Answer
The value of is 205 Hz.