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A stretched string resonates with tuning fork frequency $512\; Hz$ when length of the string is $0.5\; m$. The length of the string required to vibrate resonantly with a tuning fork of frequency $256 \;Hz$ would be .......... $m$
An organ pipe ${P_1}$ closed at one end vibrating in its first overtone and another pipe ${P_2}$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of ${P_1}$ and ${P_2}$ is
Two sources of sound of same frequency are placed at a distance of $100\,m$ from each other. An observer moving in between them hears $4$ beats per second. If the distance between the sound sources is increased to $400\,m$, then number of beats heard by him will be :-
A string of length $1\ m$ fixed at both ends is vibrating in $3^{rd}$ overtone. Tension in string is $200\ N$ and linear mass density is $5\ gm/m$ . Frequency of these vibrations is ..... $Hz$
A stationary wave is represented by $y=A \sin (100 t) \cos (0.01 x)$, where $y$ and $A$ are in millimetres, $t$ is in second and $x$ is in metre. The velocity of the constituent wave is ........... $m / s$
A closed pipe of length $10 \,cm$ has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe ......... $cm$