$A$ composite string is made up by joining two strings of different masses per unit length $\mu$ and $4\mu$. The composite string is under the same tension. $A$ transverse wave pulse $Y = (6 \text{ mm}) \sin(5t + 40x)$,where $t$ is in seconds and $x$ in meters,is sent along the lighter string towards the joint. The percentage of power transmitted to the heavier string through the joint is approximately ..... $\%$

$A$ massless rod is suspended by two identical strings $AB$ and $CD$ of equal length. $A$ block of mass $m$ is suspended from point $O$ such that $BO$ is equal to $x$. Further,it is observed that the frequency of the $1^{st}$ harmonic (fundamental frequency) in $AB$ is equal to the $2^{nd}$ harmonic frequency in $CD$. Then,the length of $BO$ 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):

The persistence of sound in a room after the source of sound is turned off is called reverberation. The measure of reverberation time is the time required for sound intensity to decrease by $60 \,dB$. It is given that the intensity of sound falls off as $I = I_0 \exp(-c_1 \alpha)$,where $I_0$ is the initial intensity,$c_1$ is a dimensionless constant with value $1/4$. Here,$\alpha$ is a positive constant which depends on the speed of sound $v_s$,volume of the room $V$,reverberation time $t$,and the effective absorbing area $A_e$. The value of $A_e$ is the product of the absorbing coefficient and the area of the room. For a concert hall of volume $V = 600 \,m^3$,the value of $A_e$ (in $m^2$) required to give a reverberation time of $t = 1 \,s$ is closest to (speed of sound in air $v_s = 340 \,m/s$):

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 $N$)

Fill in the blanks:
$(i)$ For humans,the minimum wavelength of a sound wave in the audible range is nearly ...... .
$(ii)$ Only ...... waves can be propagated by a fluid medium.
$(iii)$ The distance travelled by a travelling wave having wavelength $\lambda$ and periodic time $T$,in one second is ...... .