Question

Two identical loudspeakers that are 5.00 m apart and face toward each other are driven in phase by the same oscillator at a frequency of 875 Hz. The speed of sound in the room is 344 m/s. If you start out standing midway between the speakers, find the shortest distance you can walk toward either speaker in order to hear a minimum of sound.

Answer 1

Answer:0.0982 m

Step-by-step explanation:

Given

distance between two loudspeaker is 5 m

frequency (f )=875 Hz

speed of sound (v)=344 m/s

Let
`x_0` be the smallest distance moved by observer then

Position of observer w.r.t to first speaker is

`x_1=(L)/(2)-x_0`

Position of observer w.r.t to second speaker is

`x_2=(L)/(2)+x_0`

`\Delta x=2x_0`

For Destructive interference

`\Delta x=\left (  m+(1)/(2)\right )\cdot lambda`

For minimum m=0

and
`\lambda =(v)/(f)`

`2x_0=(v)/(2f)`

`x_0=(v)/(4f)=(344)/(4* 875)=0.0983 m`