Question

Two sound speakers separated by 100 m face each other and vibrate in unison at a frequency of 85 Hz. Determine three places on a line between the speakers where you cannot hear any sound.

Answer 1

S1_____________O__________________S2

   <-------------x--------->l<--------d - x ------------>

the distance between two sources = d = 100 m

at a point x from S1 they cannot hear sound

pathe difference between the waves arriving from two sources

dx = (d -x) - x

dx = d - 2x

the waves should intefere destructively

for destructive interference path difference dx = m*lambda/2 = m*v/(2f)

d - 2x = m*v/(2f)

2x = d - m*v/(2f)

x = d/2 - mv/(4f)

m = 1 , 3, 5, 6, .........

v = speed of sound = 343 m/s

for m = 1

x1 = 100/2 - 1*343/(4*85)

x1 = 49 m

for m = 3

x2 = 100/2 - 3*343/(4*85)

x2 = 47 m

for m = 5

x3 = 100/2 - 5*343/(4*85)

x3 = 45 m