Calculating Wavelength and Understanding Sound Interference in a Room

In summary: You would hear variations in volume as you move across the room, as some areas would have constructive interference (louder) and others would have destructive interference (softer). This process is called "wave interference".
  • #1
fran1942
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Homework Statement


two speakers which are placed 5m apart at one end of a large room are connected to a signal generator which puts out a 2kHz sinusoidal waveform. Calculate the wavelength of the sound.

The second part of this question is:
describe what a person would hear as he moves slowly across the room in front of the speakers and technical name for the interaction process involved.

Homework Equations


speed of sound in air 330m/s
v = λf

The Attempt at a Solution


rearranging wave equation to λ= v/f.
I filled in the values for velocity and frequency eg:
λ = 330m/s / 2kHz
which gave me an answer of .165 metres for the original question.
Can someone please advise if I have this correct or am I missing something.

My answer for the second part of the question:
I 'think' the answer would be: a slight shift in frequency due to the "Doppler effect" ?

Thanks for any help.
 
Last edited:
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  • #2
The first part is correct.

The second part sounds correct, though I am not positive.

EDIT: Actually, there would not be a change in frequency. You would hear the sound sooner, but the frequency (and wavelength) would remain the same.
 
  • #3
The key phrase is "interaction process". Doppler not significant and not the point of the question. Instead of "moves slowly across the room" consider "stands still at various locations across the room"
 
  • #4
thanks for that.
So answering the second question:
"describe what a person would hear as he moves slowly across the room in front of the speakers and technical name for the interaction process involved".

I wouldanswer:
"the person would hear an amplified sound due to the superposition of identical soundwaves coming from two different sources at the same frequency/wavelength. The technical name for that being 'amplification '."

Does that sound like a valid answer to that question ?
 
  • #5
No, that's not it. Think about what happens when you throw a single pebble into a still pond. Now instead of just one pebble, what happens when you throw two pebbles into a still pond separated by some distance, say "5m apart".
 
  • #6
Thanks, I have thought about it some more and think I understand now.

I would say you get constructive and destructive interference on the waves as each opposing wave interacts with the other.
This would demonstrate the principle of superposition (constuctive and destructive interference).

I am just not sure how this would 'sound'. Would it mean that as you stood in different parts of the room the volume would be louder or softer depending on the wave interference from each speaker ?Thanks for your help.
 
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  • #7
fran1942 said:
Would it mean that as you stood in different parts of the room the volume would be louder or softer depending on the wave interference from each speaker?

That' pretty much it!
 

1. What is the formula for calculating wavelength?

The formula for calculating wavelength is: Wavelength = Speed of Light / Frequency. This formula is represented as λ = c/v, where λ is wavelength in meters (m), c is the speed of light in meters per second (m/s), and v is frequency in hertz (Hz).

2. How do you determine the speed of light in the formula?

The speed of light is a constant value that is equal to 299,792,458 meters per second (m/s). This value is used in the formula for calculating wavelength because light always travels at this speed in a vacuum.

3. What is the relationship between wavelength and frequency?

Wavelength and frequency are inversely proportional to each other. This means that as wavelength increases, frequency decreases, and vice versa. This relationship is represented in the formula for calculating wavelength, where wavelength is in the numerator and frequency is in the denominator.

4. How is wavelength measured?

Wavelength is measured in units of length, such as meters (m), centimeters (cm), or nanometers (nm). The specific unit used depends on the scale of the wavelength being measured. For example, visible light has a wavelength range of 400-700 nanometers, while radio waves can have wavelengths in the range of meters to kilometers.

5. What is the significance of wavelength in science?

Wavelength is an important concept in science as it helps us understand and study the properties and behaviors of light and other electromagnetic radiation. It is also used in various fields such as telecommunications, astronomy, and spectroscopy.

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