The frequency of a stretched uniform wire of length $L$ under tension is in resonance with the fundamental frequency of a closed pipe of same length. If the tension in the wire is increased by $8 \ N$,it is in resonance with the first overtone of the same closed pipe. The initial tension in the wire is (in $N$)

$A$ wave is travelling along a string. At an instant,the shape of the string is as shown in the figure. At this instant,point $A$ is moving upwards. Which of the following statements is/are correct?

$A$ pipe closed at one end has a length of $0.8 \ m$. At its open end,a $0.5 \ m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \ N$ and the speed of sound is $320 \ m/s$,the mass of the string is: (in $g$)

An air column in a tube $32 \,cm$ long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length $66 \,cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):

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

In a large room,a person receives direct sound waves from a source $120 \ m$ away from him. He also receives waves from the same source which reach him after being reflected from the $25 \ m$ high ceiling at a point halfway between them. The two waves interfere constructively for wavelengths of