
Pressure node = _______ antinode and vice versa
2 cases regarding the two ends of the air columns:
(State the cases)
In case 2, where one end is open and the other closed (a type of displacement function), where is the displacement node vs displacement antinode?
 displacement antinode
 Case 1: Both ends open, e.g. flute
 Case 2: one end opened and one end close, e.g. pipe organ
 Displacement Node at closed end
 Displacement Antinode at open end

In Case 1 (both ends open), both ends are ________ ________. State the formula for the natural frequencies, f_{n} and that of λ_{n }and what harmonics are to be expected
 displacement antinodes


In Case 2: Pipe open at one end
The closed end is a ________ _______. The open end is a _______ _______. State the formula for f_{n} and λ_{n }and state the n series
 displacement node
 displacement antinode


Depict the first, second and third resonance of the following

Musicians called f_{2},f_{3},...f_{n} overtones
f_{2} = ______ harmonic = ______ overtone
f_{3} = ______ harmonic = ______ overtone



 a) f = v/λ_{1} = v/2L
 b) f = v/λ_{1} = v/2L
 c) f = v/λ_{1} = v/4L
 ∴ a=b>c

 Lowest frequency is the fundamental frequency f_{1} = v/2L
 A is wrong, if we use a thicker string, μ increases and v = (√T/μ) decreases, so f_{1} decreases
 **B** is right, increasing tension increases v which is directly proportional to f_{1}
 C is wrong, plucking the string harder only increases Amplitude
 D is wrong increasing L would decrease fundamental freq. (v/2L)


To simplify the mathematical expressions, we take x = 0, Φ_{10} = Φ_{20} = π
State the formulas for:
D_{1}
D_{2}
D (be sure to specify which portion is the lower frequency and which is the higher frequency)

Temporal interference occurs when the interfering waves have ______ ______ frequencies.
Define Beating and Beat frequency (state the formula and explain)
The human ear can detect a beat frequency up to about ____ beats/second
 slightly different frequencies
 Beating: the periodic variation in amplitude at a given point due to the supersposition of two waves having slightly different frequencies
 Beat frequency: the number of amplitude maxima one hears per second, it is the difference between the frequencies of the two sources
 f_{beat} = f_{1}  f_{2}
 20 beats/second

Restate the beat frequency formula and state the formula for amplitude modulation here (purple arrow):
 f_{b} = f_{1}  f_{2}
 The amplitude is slowly modulated as 2acos2πf_{b}t

At the 1st point, the waves are in _____. There is _______ interference. At the 2nd point, the waves are ____ ____ _____. There is _______ interference. At the 3rd point, the waves are _____ _____ _____. There is _______ interference. What would this look like if we had a superposition of the two sound waves
 phase
 constructive interference
 out of phase
 destructive interference
 back in phase
 constructive interference

This medium oscillates _____ at frequency f _{osc}. The amplitude is ______ ______ at frequency f _{beat}.
 rapidly
 slowly modulated

 f_{b} = f_{1}f_{2}
 f_{b} = 340  341
 f_{b} = 1Hz or 1s^{1}
 T = 1/fb = 1/1s^{1} = 1s


