Question

Speakers A and B are vibrating in phase. They are directly facing each other, are 1.29 m apart, and are each playing a 725 Hz tone. The speed of sound is 343 m/s. On the line between the speakers there are points where minimum sound intensity occurs. What is the distance of the nearest point from speaker A?

Answer 1

Answer: 0.054 m (or) 5.40 cm <<<<<<<<-----Answer

let
d = 1.29 m
f = 725 Hz
v = 343 m/s

wavelength of the sound, lamda = v/f

= 343/725

= 0.473 m

let x is the distance from speaker A where minimum sound intensity occurs.

path diffrence = n*lamda/2   (n = 1,3,5,7....)

(d - x) - x = n*lamda/2

(d - 2*x) = n*0.473/2

2*x = d - n*0.473/2

x = d/2 - n*0.473/4

= 1.29/2 - n*0.473/4

if n = 1,

x = 1.29/2 - 1*0.473/4

= 0.527 m

if n = 3,

x = 1.29/2 - 3*0.473/4

= 0.290 m

if n = 5,

x = 1.29/2 - 5*0.473/4

= 0.054 m (or) 5.40 cm <<<<<<<<<<<<<<<------------------------Answer

if n = 7,

x = 1.29/2 - 7*0.473/4

= -0.183 m