In Quincke's tube,a detector detects minimum intensity. Now,one of the tubes is displaced by $5 \, cm$. During displacement,the detector detects maximum intensity $10$ times,and finally a minimum intensity (when displacement is complete). The wavelength of sound is .... $cm$.

The wavelength of light in the visible part $(\lambda_V)$ and for sound $(\lambda_S)$ are related as:

$A$ clamped string is oscillating in the $n^{th}$ harmonic,then

$A$ parallel beam of light is incident on a tank filled with water up to a height of $61.5 \,mm$ as shown in the figure below. Ultrasonic waves of frequency $0.5 \,MHz$ are sent along the length of the water column using a transducer placed at the top and they form longitudinal standing waves in the water. Which of the schematic plots below best describes the intensity distribution of the light as seen on the screen? (Take the speed of sound in water to be $1500 \,m/s$)

Four different independent waves are represented by $(i)$ $y_1 = a_1 \sin \omega t$,$(ii)$ $y_2 = a_2 \sin 2\omega t$,$(iii)$ $y_3 = a_3 \cos \omega t$,and $(iv)$ $y_4 = a_4 \sin (\omega t + \frac{\pi}{3})$. With which two waves is interference possible?

$A$ hollow pipe of length $0.8 \ m$ is closed at one end. At its open end,a $0.8 \ m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the string is $50 \ N$ and the speed of sound in air is $320 \ m/s$,the mass of the string is: (in $g$)