How Close Must You Stand to Not Hear Sound from Two Separated Speakers?

[bio.student24]

PLEASE HELP! Speakers and Sound--- simple problem!

Two radio speakers produce sound with a wavelength of 0.800 m. If the two speakers are separated by 1.00 m as shown in the diagram, how close to speaker A can a person stand and not hear the sound they produce?

DIAGRAM:

[A] --------d---------- person
|
|
|


where [A] and are the speakers (they are 1.00 m apart)

The answer is d=1.05m

How do i solve this problem?

i know that in order not to hear sound, it must be destructive interference, so when the wavelengths reach the person, they must be out of phase = [m + 0.5(lambda)] where m=0,1,2...

I don't know what kind of formula to use... please help! :(

 

[kuruman]

For destructive interference, the path length difference from the sources to the person must be λ/2, or 3λ/2 or 5λ/2 or any odd number multiplied by λ/2. Here you want the closest distance the person can be, so the path length difference must be λ/2. Can you find the path length difference?

 

[bio.student24]

Path length difference = λ/2 = 0.8/2 = 0.4 m

But now what would I do?

 

[bio.student24]

I'm not sure if this is the 'correct' method... but if i use a² + b² = c²

then 1² + x² = (x+0.4)²
1 - 0.8x -0.16 = 0
x= 0.84/0.8 = 1.05 m

 

[kuruman]

I'm not sure if this is the 'correct' method... but if i use a² + b² = c²

then 1² + x² = (x+0.4)²
1 - 0.8x -0.16 = 0
x= 0.84/0.8 = 1.05 m

If L₁ is the distance from the person to the closest speaker and L₂ is the distance to the farthest speaker, then the path length difference is L₂ - L₁. Can you find expressions for L₁ and L₂ in terms of the given quantities and according to the drawing you have posted?

 

[bio.student24]

hmmm... I've been trying but i can't think of something that works.. :(

 

[kuruman]

hmmm... I've been trying but i can't think of something that works.. :(

In your drawing you have a triangle marked by the vertices "a", "b" and "person". Which side should be labeled L₁ and which side should be labeled L₂?

 

[bio.student24]

L₂ should be the distance between speaker b and the person.
L₁ should be the distance between speak a and the person.
right? now what?

 

[kuruman]

Back to my earlier posting.

If L₁ is the distance from the person to the closest speaker and L₂ is the distance to the farthest speaker, then the path length difference is L₂ - L₁. Can you find expressions for L₁ and L₂ in terms of the given quantities and according to the drawing you have posted?

 

[bio.student24]

the only thing i can think of is using Pythagorean theorem for this question..

is there a specific formula or expression relating sound waves and path length difference? i don't know one...

 

[kuruman]

Use the Pythagorean theorem and find the difference between the two lengths. That difference should be set equal to half a wavelength. Solve the equation to find d.

 

[bio.student24]

thats exactly what i did? haha
thanks :P

 

[kuruman]

So what's the answer?

 

[bio.student24]

d= 1.05 m