Question

Suppose we had two speakers, one placed some distance directly behind the other andboth pointing along the same direction, facing us. Now, we connect the speakers tothe same source and turn them on producing a single continuous tone of 440Hz. If thespeed of sound in air is about 343m/s, then how far would we have to put the backspeaker behind the front one so that weneverhear the tone when standing anywheredirectly in front of the speakers?

Answer 1

Answer:

d= 0.3898 m

Explanation:

given,

frequency of the wave = 440 Hz

speed of the sound = 343 m/s

wavelength of the wave = ?

v = λ x f

$\lambda = \dfrac{v}{f}$

$\lambda = \dfrac{343}{440}$

λ = 0.7795 m

distance where he should be standing

if you line them up you will see the waves have cancelled each other out

if two speaker are lined together  

The speed of sound in the air has no relevance on this question as it would not matter how fast the waves traveled but only that they travel at the same speed as each other.

The distance of half a wavelength in this case is

d = λ/2

 d = 0.7795/2

d= 0.3898 m