Answer

Verified

348.6k+ views

**Hint:**In order to this question, to know the velocity of sound in the air, we should apply the formula of resonance with both the given lengths of air columns separately. Now, we can calculate the velocity of sound in air.

**Complete step by step answer:**

Let the lengths of the air columns are $16\,cm\,and\,49\,cm$ be ${l_1}\,and\,{l_2}$ respectively. And also the end correction of the resonance be $e$. So,

${l_1} + e = \dfrac{v}{{4f}}$ ….eq(i)

Here, $v$ is the velocity of sound in the air and $f$ is the frequency.

Again,

${l_2} + e = \dfrac{{3v}}{{4f}}$ ….eq(ii)

So, by subtracting eq(i) from eq(ii)-

${l_2} - {l_1} = \dfrac{{3v}}{{4f}} - \dfrac{v}{{4f}} \\

\Rightarrow {l_2} - {l_1} = \dfrac{{2v}}{{4f}} \\

\Rightarrow {l_2} - {l_1}= \dfrac{v}{{2f}} \\

\Rightarrow v = 2f({l_2} - {l_1}) \\ $

So, $f$ is given in the question itself i.e.. $500\,Hz$ .

$\Rightarrow v = 2 \times 500(49 - 16) \\

\Rightarrow v = 1000(33) \\

\therefore v = 33000\,cm{s^{ - 1}}\,or\,330\,m{s^{ - 1}} $

Therefore, the velocity of the sound in air is $330\,m{s^{ - 1}}$.

**Hence, the correct option is C.**

**Note:**The length $l$ of a pipe or tube (air column) determines its resonance frequencies. Given the requirement of a node at the closed end and an antinode at the open end, only a limited number of wavelengths can be accommodated in the tube.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE