$A$ vibrating string of certain length $l$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75 \ cm$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $n$. Now,when the tension of the string is slightly increased,the number of beats reduces to $2$ per second. Assuming the velocity of sound in air to be $340 \ m/s$,the frequency $n$ of the tuning fork in $Hz$ is:

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):

$A$ pipe open at one end has a length of $0.8 \text{ m}$. At the open end of the tube, a string $0.5 \text{ m}$ long is vibrating in its first overtone and resonates with the fundamental frequency of the pipe. If the tension in the string is $50 \text{ N}$, what is the mass of the string (in $\text{ g}$)? (Neglect end correction, Speed of sound = $320 \text{ m/s}$)

Which of the following statements is incorrect?

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions at a right angle to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at the point $D$ where a detector is placed. If a minimum is formed at the detector,then the magnitude of the wavelength $\lambda$ of the wave produced is given by:

An object of density $2000 \ kg \ m^{-3}$ is hung from a thin light wire. The fundamental frequency of the transverse waves in the wire is $200 \ Hz$. If the object is immersed in water such that half of its volume is submerged,then the fundamental frequency of the transverse waves in the wire is (in $Hz$)