Q231 / 240 · KCET 2026 · Physics
A source of frequency $\nu$ gives $6$ beats/second when sounded with a source of frequency $200$ Hz. The second Harmonic of frequency $2\nu$ of the source gives $8$ beats/second when sounded with a source of frequency $420$ Hz. The value of $\nu$ is
- A$205$ Hz
- Correct answerB$206$ Hz
- C$195$ Hz
- D$210$ Hz
Solution
Given that the source of frequency $\nu$ gives $6$ beats/second with a source of $200$ Hz:
$\nu = 200 \pm 6$
$\Rightarrow \nu = 206$ Hz or $194$ Hz
The second harmonic of the source has a frequency of $2\nu$. It gives $8$ beats/second with a source of $420$ Hz:
$2\nu = 420 \pm 8$
$\Rightarrow 2\nu = 428$ Hz or $412$ Hz
$\Rightarrow \nu = 214$ Hz or $206$ Hz
The common value satisfying both conditions is $\nu = 206$ Hz.
Answer: $206$ Hz
$\nu = 200 \pm 6$
$\Rightarrow \nu = 206$ Hz or $194$ Hz
The second harmonic of the source has a frequency of $2\nu$. It gives $8$ beats/second with a source of $420$ Hz:
$2\nu = 420 \pm 8$
$\Rightarrow 2\nu = 428$ Hz or $412$ Hz
$\Rightarrow \nu = 214$ Hz or $206$ Hz
The common value satisfying both conditions is $\nu = 206$ Hz.
Answer: $206$ Hz
Hence, the correct answer is option: 'B'.