Question

A resonance tube of length $1m$ is resonated with tuning with a tuning fork of frequency $300Hz$. If the velocity of sound in air is $\dfrac{{300m}}{{{s^{ - 1}}}}$ then the number of harmonies produced in the tube will be.
(A) $1$
(B) $2$
(C) $3$
(D) $4$

Answer 1

Harmonies: Harmonies are the generated term used to describe the distinction of a sinusoidal wave formed by waveforms of different frequencies.
Resonance Harmonies: Resonance Harmonies is a multi potential pattern formation principle, that is the same mechanism that generates the fundamental resonance, can also create a range of patterns declined harmonies by the same essential principle.

Complete step by step answer:
We have to from the formula,
${L_1} = \dfrac{\lambda }{4} = \dfrac{1}{4} = 0.25m, \\\ {L_2} = \dfrac{{3\lambda }}{4} = \dfrac{1}{4} = 0.75m, \\\$
We get,

$\lambda = \dfrac{v}{f}\;{\text{ = }}\dfrac{{300}}{{300}}{\text{ = 1m}}{\text{.}}$

Let the lengths of resonant columns be${L_1}$, ${L_2}$ and ${L_3}$ therefore
For first resonance,

${L_1} = \dfrac{\lambda }{4} = \dfrac{1}{4} = 0.25m,$
For second resonance,

${L_2} = \dfrac{{3\lambda }}{4} = \dfrac{1}{4} = 0.75m,$
For third resonance.

${L_3} = \dfrac{{5\lambda }}{4} = \dfrac{1}{5} = 1.25m,$

It is clear that only two harmonies are possible because ${L_3}$ is greater than the total length $1m$ of the tube.

So, the correct answer is “Option B”.

Note:
The frequencies of the various harmonies are multiple of the frequency of the first harmonic; each harmonic frequency (${f_n}$) is given by the equation ${f_n} = n{f_1}$.