Question

PLEASE SHOW ALL WORK AND EXPLAIN!!! THANKS!!!

5. Two large speakers face each other.  They are 100m apart and each are sounding the same note. Standing midway between the speakers you do nothear a sound.  You start to walk towards one of the speakers at speed of 2m/sec.  The sounds start to increase and is the loudest when you've moved 75cm from your starting point.

      a. What is the note the speakers are playing?

      b. As you continue to walk, what is the beat frequency you hear? (if you cannot do part a, then assume the frequency is 200 Hz)

Answer 1

a) The two speakers are out of phase. Because, at mid point distructive interfrence is taking place.

so, 75 cm = lamda/2

==> lamda = 2*75 cm

= 150 cm

= 1.5 m

we know, speed of soubd, v = 343 m/s

so, the note the speakers are playing f = v/lamda

= 343/1.5

= 228.7 Hz <<<<<<<<<<--------------Answer

b) v = 2 m/s (velocity of obsrver)

frequency heard from the front speaker, f' = f*(v_sound + v)/v_sound

= 228.7*(343 + 2)/343

= 230.0 Hz

frequency heard from the back speaker, f'' = f*v_sound/(v_sound + v)

= 228.7*343/(343 + 2)

= 227.4 Hz

so, beat frequency heard, f' - f'' = 230.0 - 227.4

= 2.60 Hz <<<<<<<<--------------Answer