Find the deadspot from distance from the speaker

[nickb145]

Homework Statement

You're midway between two loudspeakers producing sound with the same 83.5cm wavelength, and you experience constructive interference.

How far must you move toward one speaker in order to find a dead spot?

Homework Equations

The Attempt at a Solution

I have no clue what to do. I've done all the other problems on my HW just fine..but not this...
All i have is the wavelength. not sure what to do..I'm sure it's simple...probably haven't thought about it clearly..

 

[Basic_Physics]

A standing wave is set up between the 2 speakers.

 

[CWatters]

Google for constructive and destructive interference.
Work out the conditions required for both.
Make a drawing.

 

[hjelmgart]

At least you don't need to think about beating effects, as the waves have the same frequency. Have you worked with interference before? I am uncertain, if you can simply assume they are plane waves or not. I think sound waves are usually spherical, but perhaps you can assume, that they are plane waves, if you are far from the speakers.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/interf.html#c4

 

[Nickie]

I would approach this problem by first understanding the concept of constructive and destructive interference. When two waves with the same wavelength meet, they can either add up (constructive interference) or cancel each other out (destructive interference) depending on their relative positions.

In this scenario, the two speakers are producing sound waves with the same wavelength. When you are standing in the middle, you experience constructive interference, meaning the waves are adding up to produce a louder sound. However, as you move towards one speaker, the distance between you and that speaker decreases, causing the waves to no longer be in phase and resulting in destructive interference. This is when you would experience a dead spot, where the sound is significantly quieter.

To find the distance from the speaker where the dead spot occurs, we can use the concept of phase difference. When two waves are in phase, they have a phase difference of 0 degrees. As you move away from the midpoint, the phase difference between the two waves increases. At the point of destructive interference, the phase difference is 180 degrees.

Using the wavelength (83.5cm) and the phase difference (180 degrees), we can calculate the distance from the speaker using the following equation:

d = (λ/2) * (180/360)

where d is the distance from the speaker and λ is the wavelength.

Plugging in the values, we get:

d = (83.5cm/2) * (180/360)

d = 41.75cm

Therefore, to find the dead spot, you would need to move 41.75cm towards one of the speakers. I hope this helps you understand the problem better. If you have any further questions, please let me know.