KCET · Physics · Waves and Sound
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
- B \(206\) Hz
- C \(195\) Hz
- D \(210\) Hz
Answer & Solution
Correct Answer
(B) \(206\) Hz
Step-by-step Solution
Detailed explanation
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
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