What Is the Resulting Frequency When Two Different Sound Frequencies Combine?

  • Thread starter Thread starter erisedk
  • Start date Start date
  • Tags Tags
    Frequency
AI Thread Summary
When two sound sources with slightly different frequencies n1 and n2 are played together, the resulting frequency perceived is (n1+n2)/2. The discussion initially confused this phenomenon with beats, but it was clarified that the combined sound results from the addition of sine waves. The mathematical representation of this combination reveals that the frequency is indeed the average of the two. The amplitude variations perceived by the listener are not considered traveling components, but rather as changes in loudness. Understanding this concept is crucial for grasping how sound waves interact.
erisedk
Messages
372
Reaction score
7

Homework Statement


When two sound sources of the same amplitude but of slightly different frequencies n1 and n2 are sounded simultaneously, the sound one hears has a frequency equal to

Ans: (n1+n2)/2

Homework Equations

The Attempt at a Solution


I have virtually no clue how that's the answer. I thought maybe the problem was related to beats, but it's clearly not. Beyond this, I just don't know at all.
 
Physics news on Phys.org
erisedk said:

Homework Statement


When two sound sources of the same amplitude but of slightly different frequencies n1 and n2 are sounded simultaneously, the sound one hears has a frequency equal to

Ans: (n1+n2)/2

Homework Equations

The Attempt at a Solution


I have virtually no clue how that's the answer. I thought maybe the problem was related to beats, but it's clearly not. Beyond this, I just don't know at all.
No, it is related to beats. Write the expression for the addition of two sine waves. What trigonometric formulae do you know that look relevant?
 
Got it! Asin(2πn1t-kx) + Asin(2πn2t-kx) = 2Asin(πn1t+πn2t2-kx)cos(πn1t-πn2t), which will have the frequency (n1+n2)/2
As for cos(πn1t-πn2t), is it something like variable amplitude term in standing wave equations? Cos it doesn't have any traveling component.
 
erisedk said:
Got it! Asin(2πn1t-kx) + Asin(2πn2t-kx) = 2Asin(πn1t+πn2t2-kx)cos(πn1t-πn2t), which will have the frequency (n1+n2)/2
As for cos(πn1t-πn2t), is it something like variable amplitude term in standing wave equations? Cos it doesn't have any traveling component.
Not exactly. Your equations are not quite right. The two waves being added should have the same speed.
But whether the beat factor in the product form travels is not relevant. The listener is presumed stationary. It's a perception question; the low frequency factor is heard as variation in amplitude, not as a tone.
 
haruspex said:
Not exactly. Your equations are not quite right. The two waves being added should have the same speed.
Oh yeah, v=w/k, and so we can adjust the k's accordingly, which makes the frequency term look like this: sin(πn1t+πn2t2-(k1-k2)/2x).
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Same frequency sounding different
Replies
23
Views
3K
A question about wave motion and beat frequency
Replies
43
Views
7K
Doppler effect and beat frequency
Replies
3
Views
2K
Travelling towards a Canyon Wall: Calculating Beat Frequency
Replies
3
Views
2K
Sound Wave Interference and Finding the Path Differences with Diagrams
Replies
20
Views
5K
What is the smallest frequency difference that can be detected by the human ear?
Replies
13
Views
2K
What Was the Initial Frequency of the Trumpet Player?
Replies
2
Views
5K
What Is the Frequency of Tuning Fork B When Tuned with Wax If A Is 212 Hz?
Replies
22
Views
5K
Measuring the Speed of Sound: Examining the Frequency of Clicks
Replies
3
Views
4K
Resultant amplitude for waves of different frequencies?
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top