Question

Your idiot friend won’t calm down. So the police officer fires her revolver in the air to get his attention. Then she blows over the top of the gun barrel to dispel the smoke coming from it. When she does this, you distinctly hear the fundamental mode of the gun barrel resonate at 1.352 kHz (you really have amazing hearing, by the way).

(a) If we treat the gun barrel as a cylinder which is open at one end and closed at the other, how long is the barrel? (Assume that the speed of sound is 343 m/s.)

(b) What are the next three lowest resonances of the gun barrel?

(c) Officer McBang opens the cylinder of her revolver to reload. This effectively shortens the barrel by 2 cm and opens the end that used to be closed. Now what is the frequency of the first harmonic resonance of the barrel?

d) While Officer McBang’s stationary car emits a siren at a frequency of 751.255 Hz, another police car approaches with their siren running. You hear the sirens beat at a beat frequency of 19.2 Hz. How fast the the other car going?

Answer 1

a)

Length of barrel

Fundamental frequency of closed pipe

Length of barrel

b)

Resonant frequencies are

Next three lowest resonances of gun barrel are

c)

Effective length of barrel is reduced by 2cm, , that is

Now the barrel is open at both ends. Fundamental frequency of barrel (first harmonic )

d)

Frequency of siren from stationary car(at rest)

Frequency of siren from approaching car

Beat frequency