An open organ pipe having fundamental frequency (n) is in unison with a vibrating string. If the tube is dipped in water so that $$75 \%$$ of the length of the tube is inside the water then the ratio of fundamental frequency of the air column of dipped tube with that of string will be (Neglect end corrections)

In case of a stationary wave pattern which of the following statement is CORRECT?

If the length of stretched string is reduced by $$40 \%$$ and tension is increased by $$44 \%$$ then the ratio of final to initial frequencies of stretched string is

Consider the Doppler effect in two cases. In the first case, an observer moves towards a stationary source of sound with a speed of $$50 \mathrm{~m} / \mathrm{s}$$. In the second case, the observer is at rest and the source moves towards the observer with the same speed of $$50 \mathrm{~m} / \mathrm{s}$$. Then the frequency heard by the observer will be

[velocity of sound in air $$=330 \mathrm{~m} / \mathrm{s}$$.]