Question

A student performed the experiment to measure the speed of sound in air using the 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,

• A. The intensity of the sound heard at the first resonance was more than that at the 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 ends of the prongs is typically around $1cm$
• D. The length of the air column at the first resonance was somewhat shorter than ${\frac{1}{4}}^{th}$ of the wavelength of the sound in the air

Answer 1

The correct option is D

The length of the air column at the first resonance was somewhat shorter than ${\frac{1}{4}}^{th}$ of the wavelength of the sound in the air

The explanation for the correct options

Options A and D-

1. The length of the second resonance is greater than the length of the first resonance.
2. The larger the length of the resonance, the feebler the intensity.
3. Therefore, the intensity of the sound heard at the first resonance was more than at the second resonance.
4. $L\propto \frac{1}{I}$
5. The length of the resonance, $L$ is inversely proportional to the intensity, $I$.
6. Length of the air column at the first resonance, $l+e=\frac{\lambda }{4}$ [Where, $\lambda$ is the wavelength and $e$ is the end correction.]

The explanation for the incorrect options

Option B- The prongs of the tuning fork should be placed in a vertical plane above the resonance tube to create longitudinal waves.

Option C- Since to determine amplitude we need the difference between the height of air columns that is not given in the question.

Hence, the correct option is A and D.