KCET · Physics · Thermodynamics
A pipe of \( 30 \mathrm{~cm} \) long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a \( 1.1 \mathrm{kHz} \) source ? Given speed of sound in air \( =330 \mathrm{~ms}^{-1} \).
- A Fifth harmonic
- B Fourth harmonic
- C Third harmonic
- D Second harmonic
Answer & Solution
Correct Answer
(D) Second harmonic
Step-by-step Solution
Detailed explanation
Given, length of pipe, \(L=30 \mathrm{~cm}=30 \times 10^{-2} \mathrm{~m}\); frequency, \(f=1.1 \mathrm{kHz}=1.1 \times 10^{3} \mathrm{~Hz}\); speed of sound,
\(v=330 \mathrm{~ms}^{-1}\)
We know \(f=n \times \frac{v}{2 L}\)
\(\Rightarrow 1.1 \times 10^{3}=n \times \frac{330}{2 \times 30 \times 10^{-2}}\)
\(1.1 \times 10^{3}=n \times \frac{11}{2 \times 10^{-2}}\)
\(\Rightarrow n=\frac{1.1 \times 10^{3} \times 2 \times 10^{-2}}{11}=2\)
\(v=330 \mathrm{~ms}^{-1}\)
We know \(f=n \times \frac{v}{2 L}\)
\(\Rightarrow 1.1 \times 10^{3}=n \times \frac{330}{2 \times 30 \times 10^{-2}}\)
\(1.1 \times 10^{3}=n \times \frac{11}{2 \times 10^{-2}}\)
\(\Rightarrow n=\frac{1.1 \times 10^{3} \times 2 \times 10^{-2}}{11}=2\)
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