MHT CET · Physics · Waves and Sound
The frequencies of three tuning forks A, B and C are related as \(\mathrm{n}_{\mathrm{A}}>\mathrm{n}_{\mathrm{B}}>\mathrm{n}_{\mathrm{C}}\). Which the forks \(\mathrm{A}\) and \(\mathrm{B}\) are sounded together, the number of beats produced per second is ' \(\mathrm{n}_1\) '. When forks \(\mathrm{A}\) and \(\mathrm{C}\) are sounded together the number of beats produced per second is ' \(\mathrm{n}_2\) '. How may beats are produced per second when forks B and \(\mathrm{C}\) are sounded together?
- A \(\mathrm{n}_1-\mathrm{n}_2\)
- B \(\frac{\mathrm{n}_1+\mathrm{n}_2}{2}\)
- C \(\mathrm{n}_2-\mathrm{n}_1\)
- D \(\mathrm{n}_1+\mathrm{n}_2\)
Answer & Solution
Correct Answer
(C) \(\mathrm{n}_2-\mathrm{n}_1\)
Step-by-step Solution
Detailed explanation
\(
\mathrm{n}_{\mathrm{A}}-\mathrm{n}_{\mathrm{B}}=\mathrm{n}_1
\)
\(
\mathrm{n}_{\mathrm{A}}-\mathrm{n}_{\mathrm{C}}=\mathrm{n}_2
\)
Subtracting Eq. (i) from eq. (ii)
\(
\mathrm{n}_{\mathrm{B}}-\mathrm{n}_{\mathrm{C}}=\mathrm{n}_2-\mathrm{n}_1
\)
\mathrm{n}_{\mathrm{A}}-\mathrm{n}_{\mathrm{B}}=\mathrm{n}_1
\)
\(
\mathrm{n}_{\mathrm{A}}-\mathrm{n}_{\mathrm{C}}=\mathrm{n}_2
\)
Subtracting Eq. (i) from eq. (ii)
\(
\mathrm{n}_{\mathrm{B}}-\mathrm{n}_{\mathrm{C}}=\mathrm{n}_2-\mathrm{n}_1
\)
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