The discussion revolves around the combination of two sound frequencies, specifically how their interaction results in a perceived frequency. The subject area includes wave physics and sound frequency analysis.
Some participants have made attempts to derive the resulting frequency mathematically, while others question the accuracy of the equations presented. There is an ongoing exploration of how the perceived frequency relates to amplitude variations and the stationary nature of the listener.
Participants note the assumption that the two sound waves have the same amplitude and speed, which is crucial for their analysis. There is also a discussion about the implications of the listener's position in relation to the sound waves.
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?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.
Not exactly. Your equations are not quite right. The two waves being added should have the same speed.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.
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).haruspex said:Not exactly. Your equations are not quite right. The two waves being added should have the same speed.