Recall:
Distance between node and adjacent antinode,  NA = wavelength/4
Distance between 2 adjacent nodes, NN = Distance between 2 adjacent anti-nodes, AA =  wavelength/2

Inquiry 5: We draw waves in a pipe as sinusoidal in shape like that in above graphs.
What should the two “axes” of the graphs be?


In musical instruments, the simplest mode of vibration is the fundamental frequency, f1. This is the lowest possible frequency.  This determines the frequency of the note produced since the waveform has the largest amplitude compared with the other modes of vibrations. Frequency f2 is the next higher possible frequency followed by f3. It is the superposition of all the possible modes of vibration that causes different instruments to sound different.

Eg 4 An organ pipe of effective length 0.60 m is closed at one end. Given that the speed of sound in air is 300 m s?-1. Find the two lowest resonant frequencies.


Solutions:
For fundamental mode of vibration, Length of pipe, l = NA =  
0.60 =   wavelength/4 = 2.4 m
v = f * wavelength
300 = f (2.4)
f = 125 Hz

For 1st overtone (next “complex” mode of vibration), Length of pipe, l = NANA =  
0.60 =   3*wavelength/4 = 0.80 m
v = f *wavelength
300 = f (0.80)
f = 375 Hz


Eg 5 The Tacoma Bridge was an 850 m long suspension bridge built across a river. The speed of transverse waves along the span of the bridge was 400 m s?1. Find the most possible frequency of the wind that caused the collapse of the Tacoma Bridge if it was vibrating at its fundamental frequency

Solutions:

wavelength/2  = L
wavelength = 2*850 = 1700 m

since v = f* wavelength
400 = f*1700
0.24 Hz = f


The bridge collapsed as resonance set in.
therefore Driving frequency of wind = fundamental frequency of bridge vibration = 0.24 Hz