Resonance

Resonance In a Tube

Sound waves in a tube can be looked at as standing waves of pressure, or displacement

Reflection in a Pipe

In a closed Pipe, High pressure reflects as High Pressure

In an open Pipe, High pressure is reflected as Low Pressure

The frequencies required to produce resonance in an open pipe are not the same as those required to produce resonance in a closed pipe of the same length

Closed Pipe

A closed pipe resonates when a standing wave is produced with a node on one end and an antinode on the other end

The distance between a node and an antinode is 1/4th of the wave length

The distance between antinodes is ½ of a wavelength

Open Pipe

An Open Pipe resonates when there is either a node or antinode

The distance between consecutive nodes or antinodes is one half of a wavelength

Calculation of Resonant Frequencies

The resonant frequencies in a pipe of known length can be calculated by knowing how many wavelengths are needed to resonate in a pipe

The first resonant wavelength will be equal to 4 times the length of the pipe (L)

The second will be ¾L, then 5/4L and so on.

From Wavelength to Frequency

Recall that f = v/λ

If the first wavelength is 4L, the first frequency will be the speed of sound divided by 4L

Find the lowest frequency wave that can resonate in a closed pipe of length 8m

Resonant Frequencies

For a closed pipe, the first resonance occurs when the length of the pipe is /4 meaning =4L

What is the next resonant frequency?

2nd resonant frequency in a closed pipe

f1 = v/4Lfn = (n+1)(f1)

What is the first resonant frequency in a open pipe with respect to Lf1 = v/2L

f2 = v/Lf3 = 3v/2Lf4 = 2v/Lfn = n*f1

Resonance in Musical Instruments

Musical instruments, unlike tuning forks resonate at multiple frequencies

The frequencies are the different resonant frequencies and the way that they interfere with each other gives the instrument its unique sound.

Each frequency sound wave will have a different intensity which makes the sound even more unique.

Doppler Effect

A car honks its horn as it approaches a person standing on the side of the road.

The person hears a frequency of 430Hz when the car is approaching, and a frequency of 470Hz after the car is moving away from the observer.

What is the frequency of the horn? What is the speed of the car?

Resonance And Sound

A Clarinet is a closed pipe roughly .75 m long. How long is the longest wavelength that will resonate in a clarinet? What is the frequency of the wave?What are the next two frequencies that will resonate?

Resonance

A flute is an open pipe roughly .75 m long. What is the longest wavelength that will resonate in a flute?

What is the frequency? What are the next two frequencies?

Count the WavesFind the frequency in terms of L