A source of sound emits sound waves at frequency $$f_0$$. It is moving towards an observer with fixed speed $${v_s}$$ ($${v_s},v$$, where $$v$$ is the speed of sound in air.) If the observers were to move towards the source with speed $$v_0$$, one of the following two graphs (A and B) will give the correct variation of the frequency $$f$$ heard by the observer as $$v_0$$ is changed.

The variation of $$f$$ with $$v_0$$ is given correctly by

The string of length 2 m is fixed at both ends. If the string vibrates in its fourth normal mode with a frequency of 500 Hz, then the waves would travel on it with a velocity of

The displacement of a wave is given by

$$y = 20\cos (\omega t + 4z)$$

The amplitude of the given wave is

If frequencies are $$(\nu-1)$$ and $$(\nu+2)$$, then find the value of beats.