# What Is the Phase Difference Between Two Speakers Emitting Sound Waves?

• bored2death97
In summary, the listener experiences maximum sound intensity when speaker 2 is at the origin and speaker 1 is at x=0.50m. As speaker 1 is moved forward, the intensity decreases and then increases, reaching another maximum at x=0.90m. The frequency of the sound is 850 Hz, and the phase difference between the speakers is -(∏/2). To solve for the phase difference, the equations v=λf and Δ∅= [(2∏Δd)/λ] + Δ∅o were used.
bored2death97

## Homework Statement

Two loudspeakers emit sound waves along the x-axis. a listener in front of both speakers hears a maximum sound intensity when speaker 2 is at the origin and speaker 1 is at x=0.50m. If speaker 1 is slowly moved forward, the sound intensity decreases and then increases, reaching anohter maximum when speaker 1 is as x=0.90m

A) (solved already) What is the frequency of he sound? Assume V(sound)=340 m/s

B) What is the phase difference between the speakers??

## Homework Equations

v=λf

Δ∅= [(2∏Δd)/λ] + Δ∅o

## The Attempt at a Solution

Well for A) I used v=λf. With a λ of 0.40m, I got the right answer of a frequency of 850 Hz.

For B) I am unsure as to the initial phase difference, Δ∅o.
For the record the answer is -(∏/2)

Last edited:
If you have trouble with remembering what the equations are saying, you need to go back to the physics.

You know the relative phase of the waves where the listener is standing, for example, and you also know the equation for the wave at any particular time. So work it backwards.

You can let speaker 1 output = cos(ωt), then speaker 2 output = cos(ωt - kx + ψ) at position of speaker 1, where x = distance between speakers and k = 2π/λ = ω/v, v = 340 m/s.

The argument of cos() must then be the same at distance a = 0.5m, and also (the same + 2π) at distance b = 0.9m. So just solve for ω (which you already & correctly did) and also for ψ. Reduce the computed ψ in magnitude by integer multiples of 2π as needed to drive the value to -π < ψ < +π & you will get the posted answer.

## What is the phase difference of speakers?

The phase difference of speakers refers to the difference in timing or delay between the sound waves produced by two speakers playing the same audio signal. This difference can affect the overall sound quality and perception of the audio.

## How is the phase difference of speakers measured?

The phase difference of speakers is typically measured in degrees or radians, with 360 degrees representing a full cycle of the audio waveform. This can be measured using specialized equipment or software that analyzes the audio signals from each speaker.

## What causes phase difference in speakers?

Phase difference in speakers can be caused by a variety of factors, including the distance between the speakers, their positioning in the room, and any obstacles or reflections that may affect the sound waves. It can also be affected by the design and quality of the speakers themselves.

## How does phase difference affect sound quality?

The phase difference of speakers can impact the sound quality in several ways. If the phase difference is too large, it can result in a loss of bass or muddiness in the sound. On the other hand, a small phase difference can contribute to a more balanced and immersive sound experience.

## Can phase difference be adjusted or corrected?

Yes, phase difference can be adjusted by changing the positioning or orientation of the speakers, using specialized audio equipment, or utilizing software to correct the phase difference. This can help improve the overall sound quality and balance of the audio.

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