Question

A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air column is the second resonance. Then,
(This question has multiple correct options)
A. The intensity of the sound heard at the first resonance is more than that at the second resonance
B. The prongs of the tuning fork were kept in a horizontal plane above the resonance tube
C. The amplitude of vibration of the end of the prongs is typically round 1 cm
D. The length of their column at the first resonance was somewhat shorter than ${{\dfrac{1}{4}}^{th}}$ of the wavelength of the sound in air

Answer 1

Hint: We are given a situation where a student performs an experiment to measure the speed of sound in air using resonance air-column method. It is said that the student observes the resonance with a shorter air-column as the first resonance and with the longer air column as the second resonance. We are given four different statements about the situation. By evaluating each statement with respect to the situation we can find the correct statements.

Complete answer:
In the question it is said that a student performs an experiment to measure the speed of sound in air and she uses the resonance air – column method.
From the experiment she got two resonances in the air – column by lowering the level of water.
It is observed that the resonance with the shorter air column is the first resonance and the resonance with longer air – column is the second resonance, i.e. the length of the second resonance is greater than the length of the second resonance.
Let ${{l}_{1}}$ be the length of the first resonance and ${{l}_{2}}$ be the length of the second resonance.
It is said that, ${{l}_{2}}>{{l}_{1}}$
We know that when the length of the air column is greater, then the absorption of energy will also be more. If more energy is absorbed only less energy will be left. Then the intensity of sound will be less, i.e.
As the length of the air column increases the intensity of sound will be less.
Hence in this case since the length of the second resonance is greater than the length of the second resonance, the intensity of sound heard in the second resonance will be less than the intensity of sound in the first resonance.
Therefore we can say that option A is correct.
Consider the figure of first resonance given below.

The total length of the air column is,
${{l}_{1}}+e$, where ’${{l}_{1}}$’ is the length of the first air column and ‘e’ is end correction.
We know that the total length,
${{l}_{1}}+e=\dfrac{\lambda }{4}$, were ‘$\left( \dfrac{\lambda }{4} \right)$’ is the distance between an antinode and a node and ‘$\lambda $’ is the wavelength of sound in air.
From this we get the length of first air column as,
${{l}_{1}}=\dfrac{1}{4}\lambda -e$
i.e. the length of the air column in the first resonance is somewhat shorter than $\left( \dfrac{1}{4} \right)$ times the wavelength of sound in air.

So, the correct answer is “Option A and D”.

Note:
In resonance air – column method the prongs of the tuning fork will be kept in a vertical plane above the tube. Hence option B is incorrect.
The amplitude of vibration at the end of the prongs is not predictable. Hence it is not 1 cm and therefore option C is also incorrect.