11.3. Resonance with Sound Waves http://www.ck12.org
Answer:v=λfbutf= 3 f 1 = 3 (220 Hz) =660 Hz, so
λ= 0 .60 m
v= (660 Hz)( 0 .60 m) =396 m/s.
Open and Closed Pipes and Tubes
In our discussions of pipes, the length of the pipe will be assumed to be much greater than the diameter of the pipe.
An open pipe, as the name implies, has both ends open. Though open pipes have antinodes at their ends, the resonant
conditions for standing waves in an open pipe are the same as for a string fixed at both ends. Thus for an open pipe
we have: forn= 1 , 2 , 3 ...,L=n 2 λn, orλn=^2 nL.
There is a simple experiment your instructor may have you do in class that demonstrates resonance in an open tube.
Roll two sheets of long paper into two separate tubes and use a small amount of tape to keep them rolled. Have the
diameter of one tube just small enough to fit inside the other tube so the inside tube can freely slide back and forth.
Hold a struck tuning fork (your instructor will make sure the frequency is adequate) close to the end of the outer tube
while the inside tube is moved slowly. When the total length of the tubes is the proper length to establish resonance,
you’ll hear a noticeable increase in the volume of the sound. At this moment, there are standing waves present in the
tubes.
A closed pipe is closed at only one end. Closed pipes have the same standing wave patterns as a string fixed at one
end and unbound at the other end. They therefore have the same resonant conditions as a string fixed at only one
end, forn= 1 , 3 , 5... ,L=n 4 λnorλn=^4 nL.
A closed pipe supporting the first harmonic (the fundamental frequency) will fit one-fourth of the wavelength, the
second harmonic will fit three-fourths, and so on, as shown inFigure11.23. Compare these pictures to those in the
figures above for a string fixed at only one end
FIGURE 11.23
A standard physics laboratory experiment is to find the velocity of sound by using a tuning fork that vibrates over a
closed pipe as shown inFigure11.24. The water level in a pipe is slowly changed until the first harmonic is heard.
http://demonstrations.wolfram.com/ResonanceInOpenAndClosedPipes/