A source of unknown frequency gives $4 ext{ beats/s}$ when sounded with a source of known frequency $250 e

Question

A source of unknown frequency gives $4 	ext{ beats/s}$ when sounded with a source of known frequency $250 	ext{ Hz}$. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency $513 	ext{ Hz}$. The unknown frequency is

Accepted Answer

1. **Determine possible frequencies from the first condition:** The beat frequency is the difference between the two frequencies. Let the unknown frequency be $f$. Since it produces 4 beats/s with a source of $250 	ext{ Hz}$ ,
   $$|f - 250| = 4$$
   $$f = 250 \pm 4$$
   $$f = 254 	ext{ Hz} 	ext{ or } 246 	ext{ Hz}$$
2. **Determine possible frequencies from the second condition:** The second harmonic of the unknown frequency is $2f$. This produces 5 beats/s with a source of $513 	ext{ Hz}$.
   $$|2f - 513| = 5$$
   $$2f = 513 \pm 5$$
   $$2f = 518 	ext{ Hz} 	ext{ or } 508 	ext{ Hz}$$
   $$f = 259 	ext{ Hz} 	ext{ or } 254 	ext{ Hz}$$
3. **Find the common frequency:** Comparing the possible values of $f$ from both conditions, the only common value is $f = 254 	ext{ Hz}$.
Therefore, the unknown frequency is $254 	ext{ Hz}$.

Step-by-Step Solution

Practice All PHYSICS Questions