A standing wave $y=A \sin \left(\frac{20}{3} \pi x\right) \cos (1000 \pi t)$ is maintained in a taught string, where $y$ and $x$ are in metres. The distance between two successive points oscillating with the amplitude $\frac{A}{2}$ across a node is

The fundamental frequency of an open organ pipe is $$600 \mathrm{~Hz}$$. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is $$330 \mathrm{~m} / \mathrm{s}$$, then the length of a closed organ pipe is

The wavelength of two waves are 40 and $$42 \mathrm{~cm}$$ respectively. If the temperature of the room is $$20^{\circ} \mathrm{C}$$ then what will be the number of beats produced per second by these waves. When the speed of sound at $$0^{\circ} \mathrm{C}$$ is $$332 \mathrm{~m} / \mathrm{s}$$ ?

When a string is divided into four segments of $$l_1, l_2, l_3$$ and $$l_4$$. The fundamental frequencies of these three segments are $$v_1, v_2, v_3$$ and $$v_4$$, respectively. The original fundamental frequency $$(v)$$ of the string is