Two waves $$Y_1=0.25 \sin 316 t$$ and $$Y_2=0.25 \sin 310 t$$ are propagating along the same direction. The number of beats produced per second are

Two identical strings of length $$l$$ and $$2l$$ vibrate with fundamental frequencies $$\mathrm{N} \mathrm{~Hz}$$ and $$1.5 N$$ Hz, respectively. The ratio of tensions for smaller length to large length is

When open pipe is closed from one end third overtone of closed pipe is higher in frequency by $$150 \mathrm{~Hz}$$, then second overtone of open pipe. The fundamental frequency of open end pipe will be

A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their $P^{\text {th }}$ overtone is