Calculating Wavelength and Understanding Sound Interference in a Room

[fran1942]

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.

 

[jakobsandberg]

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.

 

[lewando]

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"

 

[fran1942]

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 ?

 

[lewando]

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".

 

[fran1942]

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.

 

[lewando]

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!