Two progressive waves are travelling towards each other with velocity $$50 \mathrm{~m} / \mathrm{s}$$ and frequency $$200 \mathrm{~Hz}$$. The distance between the two consecutive antinodes is

A string fixed at both the ends forms standing wave with node separation of $$5 \mathrm{~cm}$$. If the velocity of the wave on the string is $$2 \mathrm{~m} / \mathrm{s}$$, then the frequency of vibration of the string is

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '$$L$$'. The length of the open pipe will be

A car sounding a horn of frequency $$1000 \mathrm{~Hz}$$ passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is $$11: 9$$. If the speed of sound is '$$v$$', the speed of the car is