$A$ transverse sinusoidal wave of amplitude $a,$ wavelength $\lambda,$ and frequency $n$ is travelling on a stretched string. The maximum speed of any point on the string is $v/10,$ where $v$ is the speed of propagation of the wave. If $a = 10^{-3} \ m$ and $v = 10 \ m/s,$ then $\lambda$ and $n$ are given by:

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

In the Kundt's tube experiment (shown in fig. $(i)$),the rod is clamped at the center. In the modified experiment (shown in fig. $(ii)$),the rod is clamped at the end. It is known that the speed of sound in air is $330\ m/s$,the powder piles up at successive distances of $0.6\ m$,and the length of the rod used is $1\ m$. Calculate the speed of sound in the rod in $m/s$.

Select the correct alternative$(s)$ :-
$(A)$ Number of nodes equals to number of antinodes in closed organ pipe.
$(B)$ In open organ pipe,if number of antinodes is $m$,then number of nodes will be $m-1$.
$(C)$ If frequency of $4^{\text{th}}$ harmonic of open organ pipe is $400 \ Hz$,then frequency of $2^{\text{nd}}$ overtone of closed organ pipe of same length is $250 \ Hz$.
$(D)$ Time interval between successive maxima or minima (for superposition of two waves) is $\Delta t = \frac{1}{|f_1-f_2|} \ s$.

$A$ 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 $g$)

$A$ 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?