Imagine you are in an open field where two loudspeakers are set up and connected

Question

Imagine you are in an open field where two loudspeakers are set up and connected to the same amplifier so that they emit sound waves in phase at 688 Hz. Take the speed of sound in air to be 344 m/s.
you are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left
Part B
What is the shortest distance d you need to walk forward to be at a point where you cannot hear the speakers? The forward direction is defined as being perpendicular to a line joining the two speakers and you start walking from the line that joins the two speakers.
Imagine you are in an open field where two loudspeakers are set up and connected to the same amplifier so that they emit sound waves in phase at 688 Hz. Take the speed of sound in air to be 344 m/s.
you are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left
Part B
What is the shortest distance d you need to walk forward to be at a point where you cannot hear the speakers? The forward direction is defined as being perpendicular to a line joining the two speakers and you start walking from the line that joins the two speakers.
Imagine you are in an open field where two loudspeakers are set up and connected to the same amplifier so that they emit sound waves in phase at 688 Hz. Take the speed of sound in air to be 344 m/s. Imagine you are in an open field where two loudspeakers are set up and connected to the same amplifier so that they emit sound waves in phase at 688 Hz. Take the speed of sound in air to be 344 m/s. Imagine you are in an open field where two loudspeakers are set up and connected to the same amplifier so that they emit sound waves in phase at 688 Hz. Take the speed of sound in air to be 344 m/s.
you are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left
Part B
What is the shortest distance d you need to walk forward to be at a point where you cannot hear the speakers? The forward direction is defined as being perpendicular to a line joining the two speakers and you start walking from the line that joins the two speakers.

you are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left
Part B

you are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left
Part B

Part B

Part B

Part B
What is the shortest distance d you need to walk forward to be at a point where you cannot hear the speakers? The forward direction is defined as being perpendicular to a line joining the two speakers and you start walking from the line that joins the two speakers.
What is the shortest distance d you need to walk forward to be at a point where you cannot hear the speakers? The forward direction is defined as being perpendicular to a line joining the two speakers and you start walking from the line that joins the two speakers.

Part B

Explanation / Answer

as velocity V = wavelength L * frequency f

so

Waveength L = V/f = 344/688 = 0.5 m

for Destructive interference , path difference = odd mutiples of L/2

= 0.25 , 0.75 .......

here rR^2 + Xr^2 + d^2

rL = xL^2 + d^2

path diff = rR - rL = dR = 0.5 L

(xR^2 +d^2) -(xL^2 +d^2) = L/2

(3.5^2 + d^2)^(1/2) -(9m^2 +d^2) ^(1/2) = 0.25 m

solving for d, d = 5.62 m (answer)

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