(a) Fig. 2 represents two waves with nearly equal angular frequencies w, and w2 which superimpose in water. Consider (w1 – w2) = Aw is very small. Deduce the equation for the resultant displacement. i. ii. Analyze the nature of the amplitude of the resultant wave. iii. Establish a relation between phase velocity and group velocity of the resultant wave.

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Please explain parts c, d, and e. Please include significant figures and units. Thanks for your help!

The ability to hear a "pin drop" is the sign of sensitive hearing. Suppose a 0.53 g pin is dropped from a height of 31 cm, and that the pin emits sound for 1.4 s when it lands. Part A Assuming all of the mechanical energy of the pin is converted to sound energy, and that the sound radiates uniformly in all directions, find the maximum distance from which a person can hear the pin drop. (This is the ideal maximum distance, but atmospheric absorption and other factors will make the actual maximum distance considerably smaller.) Express your answer using two significant figures. Hνα ΑΣφ ? r = km