Q.4. 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 :- D. In case of a stretched string when vibrated, frequency of first overtone is same as second harmonic.
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}}} \ldots .
For the first overtone, \lambda=l
\therefore \quad Frequency of first overtone \mathrm{n}_1=\frac{1}{l} \sqrt{\frac{\mathrm{~T}}{\mathrm{~m}}} \ldots \ldots
Comparing (i) and (ii), \mathrm{n}_1=2 \mathrm{n}