MHT CET · Physics · Waves and Sound
In fundamental mode, the time required for the sound wave to reach up to the closed end of pipe filled with air is \(t\) second. The frequency of vibration of air column is
- A \(\frac{1}{\mathrm{t}}\)
- B \(\frac{2}{\mathrm{t}}\)
- C \(\frac{3}{\mathrm{t}}\)
- D \(\frac{0.25}{\mathrm{t}}\)
Answer & Solution
Correct Answer
(D) \(\frac{0.25}{\mathrm{t}}\)
Step-by-step Solution
Detailed explanation
In fundamental mode the length of the closed tube is \(\frac{\lambda}{4}\)
Time required to travel a distance \(\frac{\lambda}{4}\) is \(\mathrm{t}\).
Hence time required to travel a distance \(\lambda\) will be \(4 \mathrm{t}\).
\(\therefore\) Time period \(\mathrm{T}=4 \mathrm{t}\)
Frequency, \(\mathrm{n}=\frac{1}{\mathrm{~T}}=\frac{1}{4 \mathrm{t}}=\frac{0.25}{\mathrm{t}}\)
Time required to travel a distance \(\frac{\lambda}{4}\) is \(\mathrm{t}\).
Hence time required to travel a distance \(\lambda\) will be \(4 \mathrm{t}\).
\(\therefore\) Time period \(\mathrm{T}=4 \mathrm{t}\)
Frequency, \(\mathrm{n}=\frac{1}{\mathrm{~T}}=\frac{1}{4 \mathrm{t}}=\frac{0.25}{\mathrm{t}}\)
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