Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

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

$254 \text{ Hz}$

$246 \text{ Hz}$

$240 \text{ Hz}$

$260 \text{ Hz}$

Step-by-Step Solution

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 $250 \text{ Hz}$ , $|f - 250| = 4$ $f = 250 \pm 4$ $f = 254 \text{ Hz} \text{ or } 246 \text{ Hz}$
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 $513 \text{ Hz}$ . $|2f - 513| = 5$ $2f = 513 \pm 5$ $2f = 518 \text{ Hz} \text{ or } 508 \text{ Hz}$ $f = 259 \text{ Hz} \text{ or } 254 \text{ Hz}$
Find the common frequency: Comparing the possible values of $f$ from both conditions, the only common value is $f = 254 \text{ Hz}$ . Therefore, the unknown frequency is $254 \text{ Hz}$ .

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