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 $$=330 \mathrm{~m} / \mathrm{s}$$.]

The equation of simple harmonic progressive wave is given by $$y=a \sin 2 \pi(b t-c x)$$. The maximum particle velocity will be half the wave velocity, if $$\mathrm{c}=$$

Stationary waves can be produced in