MHT CET · Physics · Waves and Sound
In case of a stationary wave pattern which of the following statement is CORRECT?
- A The distance between the consecutive nodes is equal to the wavelength.
- B In a pipe at both ends only even harmonics are present in an air column.
- C In a pipe closed at one end, all harmonics are present in an air column.
- D In case of a stretched string when vibrated, frequency of first overtone is same as second harmonic.
Answer & Solution
Correct Answer
(D) In case of a stretched string when vibrated, frequency of first overtone is same as second harmonic.
Step-by-step Solution
Detailed explanation
Frequency of first harmonic \(=\mathrm{n}=\frac{\mathrm{v}}{\lambda}=\frac{1}{2 l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}\) Frequency of second harmonic \(=2 \mathrm{n}=\frac{1}{l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}.... (i)\)
For the first overtone, \(\lambda=l\)
\(\therefore \quad\) Frequency of first overtone \(\mathrm{n}_1=\frac{1}{l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}.... (ii)\)
Comparing (i) and (ii),
\(\mathrm{n}_1=2 \mathrm{n}\)
For the first overtone, \(\lambda=l\)
\(\therefore \quad\) Frequency of first overtone \(\mathrm{n}_1=\frac{1}{l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}.... (ii)\)
Comparing (i) and (ii),
\(\mathrm{n}_1=2 \mathrm{n}\)
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