Answer

Verified

372.9k+ views

**Hint:**The partially filled glass tube signifies that it is closed at one end and open at the other. A node is formed at the closed end but an antinode is formed at the open end. We shall find the end correction by finding the velocity of wave in each case and then both the equations as we are given the length of tube in its fundamental mode and at a harmonic.

**Complete answer:**

The fundamental wavelength is the wavelength at which the wave exhibits resonance for the first time. the subsequent wavelengths at which the wave shows resonance are called harmonics.

The wave velocity, $v$ is given as:

$v=\lambda \nu $

Where,

$\lambda =$ wavelength

$\nu =$ frequency of wave

In first case, length of air column $={{l}_{1}}+e$

This length is equal to one-fourth of the wavelength in the fundamental mode.

$\Rightarrow \dfrac{\lambda }{4}={{l}_{1}}+e$

$\Rightarrow \lambda =4\left( {{l}_{1}}+e \right)$

Therefore, velocity of wave is given as: $v=4\left( {{l}_{1}}+e \right)\nu $ …………. Equation (1)

In the second case, length of air column $={{l}_{2}}+e$

This length is equal to three-fourth of the wavelength in the first harmonic mode.

$\Rightarrow \dfrac{3\lambda }{4}={{l}_{2}}+e$

$\Rightarrow \lambda =\dfrac{4\left( {{l}_{2}}+e \right)}{3}$

Therefore, velocity of wave is given as: $v=\dfrac{4\left( {{l}_{2}}+e \right)\nu }{3}$ …………. Equation (2)

Since the wave velocity remains constant, thus equating equations (1) and (2),

$\Rightarrow 4\left( {{l}_{1}}+e \right)\nu =\dfrac{4\left( {{l}_{2}}+e \right)\nu }{3}$

Cancelling 4 and $\nu $from both sides, we get

$\begin{align}

& \Rightarrow \left( {{l}_{1}}+e \right)=\dfrac{\left( {{l}_{2}}+e \right)}{3} \\

& \Rightarrow 3{{l}_{1}}+3e={{l}_{2}}+e \\

& \Rightarrow 2e={{l}_{2}}-3{{l}_{1}} \\

\end{align}$

Now we have ${{l}_{1}}=0.1m$ and ${{l}_{2}}=0.35m$,

$\begin{align}

& \Rightarrow 2e=0.35-3\left( 0.1 \right) \\

& \Rightarrow 2e=0.35-0.30 \\

& \Rightarrow 2e=0.05 \\

& \Rightarrow e=\dfrac{0.05}{2} \\

\end{align}$

$\therefore e=0.025m$

**Note:**

If we create a wave in a medium that has no boundaries, this wave never meets the boundary and there is nothing stopping the wave from making a wave of any wavelength or frequency. However, if we confine this wave into a medium that has boundaries, this wave will reflect when it meets the boundary. Thus, standing waves are formed. Standing waves are formed of only selected preferred wavelengths and frequencies.

Recently Updated Pages

10 Examples of Friction in Our Daily Life

10 Examples of Evaporation in Daily Life with Explanations

The marks obtained by 50 students of class 10 out of class 11 maths CBSE

Explain the law of constant proportion in a simple way

The magnetic field due to a short magnet at a point class 12 physics JEE_Main

A transparent thin plate of polaroid is placed on another class 12 physics JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Mention the different categories of ministers in the class 10 social science CBSE

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

Give 10 examples for herbs , shrubs , climbers , creepers

Who is the executive head of the Municipal Corporation class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which monarch called himself as the second Alexander class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write an application to the principal requesting five class 10 english CBSE