Sound Waves - phase difference from time delay

In summary, to find the phase difference between two loudspeakers placed side by side, you would need to consider the frequency, speed of sound, wavelength, and time delay of the signals. In this scenario, with a time delay of 1.56 ms and a frequency of 392 Hz, the phase difference would be zero. To further understand this, one could think of the delayed signal as A sin\omega(t - td), where td is the time delay and \omega is the angular frequency.
  • #1
Arctangent
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For some reason I have trouble with questions like this. How would I get the phase difference if I were given the time delay of two loudspeakers side by side?

I'll use this question as an example:

"The speakers are now placed side by side. If the wire to speaker 1 is passed through a box that delays the signal by 1.56 ms, what is the new phase difference? "

The frequency is 392 Hz
The PD would be zero since they're beside each other
the speed is 340 m/s
the wavelengths are 0.86 m
and the time delay is 1.56 ms or 1.56e-3 s

I was able to find the period, 2.55e-3 s

But after this I kinda blank out. Any tips?
 
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  • #2
Think about what the time delay, 1.56 ms means in terms of the period, i.e. what fraction of the period, and how it relates to the wave length.

If one has a signal - A sin[itex]\omega[/itex]t, and another signal of the same form but at a delayed time of td, one could write the delayed signal as A sin[itex]\omega[/itex](t - td).
 
  • #3


I would approach this question by first understanding the concept of phase difference in sound waves. Phase difference refers to the difference in the starting point of two waves of the same frequency. In other words, it is the difference in the position of the waves at a given point in time. This can be measured in degrees or radians, and is important in understanding the interference patterns of sound waves.

In this scenario, the two speakers are emitting sound waves of the same frequency, 392 Hz. This means that they have the same wavelength, 0.86 m, and the same period, 2.55e-3 s. However, due to the time delay of 1.56 ms (1.56e-3 s) in one of the speakers, the starting point of its wave will be shifted compared to the other speaker.

To find the phase difference, we need to calculate the fraction of the wavelength that the delayed speaker is shifted by. This can be done by dividing the time delay by the period, which gives us a fraction of 0.612. This means that the delayed speaker is shifted by 0.612 wavelengths compared to the other speaker.

In terms of phase difference, this can be represented as 2π x 0.612 = 1.22π radians, or 220.3 degrees. This means that the delayed speaker's wave starts 220.3 degrees behind the other speaker's wave.

In summary, to find the phase difference given a time delay, we need to calculate the fraction of the wavelength that the delayed wave is shifted by and then convert it to radians or degrees. This allows us to understand the interference patterns and how the sound waves interact with each other. I hope this explanation helps you with your understanding of phase difference in sound waves.
 

What are sound waves?

Sound waves are a type of mechanical wave that travels through a medium, such as air or water, as a series of compressions and rarefactions. These waves are responsible for the sensation of hearing.

How does phase difference affect sound waves?

Phase difference refers to the difference in the timing or position of two waves. In sound waves, phase difference can affect the perceived loudness and direction of the sound. When the waves are in phase, they reinforce each other and the sound is louder. When they are out of phase, they cancel each other out and the sound is quieter.

What causes phase difference in sound waves?

Phase difference in sound waves can be caused by various factors, such as reflections, diffraction, and interference. For example, when sound waves reflect off of a surface, the reflected waves may have a different phase than the original waves, resulting in a phase difference.

How is phase difference measured in sound waves?

Phase difference in sound waves is measured in degrees or radians. This can be done using an oscilloscope, which displays the waveform of the sound and allows for the measurement of the phase difference between two waves.

Can phase difference be used to determine the distance of a sound source?

Yes, phase difference can be used to determine the distance of a sound source. By measuring the phase difference between the original sound wave and its reflection, the distance between the source and the reflecting surface can be calculated using the speed of sound in the medium.

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