1. Resonance Waves and Sound

2. Natural Frequency and Resonance
Natural Frequency: Oscillators have a natural frequency. This frequency is often labeled as f0 , and is also known as the resonant frequency.
For springs and pendulums it can be found by taking the inverse of the period formulas.
Resonance: When a force is repeatedly applied to an oscillator, at the resonant frequency, then the amplitude of the wave form increases with each application of force. This phenomenon it is called resonance.
Examples: A swing set. If you push with (add) a small force each time the swing reaches its greatest displacement, then the swinging motion grows and grows. This is how a singer breaks a glass with their voice. They sing a note matching the natural (resonant) frequency of a glass. This causes the glass to vibrate at its natural frequency. Each wave added by the singer increases the glasses vibration until it oscillates so much that it tears itself apart.

3. Open Tubes (open at both ends)
In wind instruments vibrating air molecules form the vibrating waves. While the waves appear very different from waves in strings they follow the same patterns. Several wave forms can be created in an open tube with a fixed length L .
mode L λ v L
1st Harmonic
2nd Harmonic
3rd Harmonic
Standing waves in open tubes consist of multiples of half wavelengths.

4. Example 2
An open tube is resonating at a fundamental frequency of 512 Hz. Determine the length of the tube.
In open tubes a half wavelength is the simplest wave form capable of creating a standing wave. Therefore, a half wavelength generates the fundamental frequency. As a result,
Substitute this into the equation for wave speed.
Substitute values and solve.
Where did v = 343 m/s come from? In string instruments the string is the medium. However, in wind instruments air as the medium. Here the speed of sound in air is known, or can be looked up in a table. Therefore, it was not given. On exams the speed of sound will be provided.

5. Closed Tubes (closes at one end, open at the other)
In wind instruments vibrating air molecules form the vibrating waves. While the waves appear very different from waves in strings they follow the same patterns. Several wave forms can be created in an open tube with a fixed length L .
mode L λ v L
1st Harmonic
2nd Harmonic
3rd Harmonic
Standing waves in closed tubes consist of the ODD multiples of quarter wavelengths.

6. Example 3
A 0.80 m long closed tube is resonating at its fundamental frequency. Determine the frequency of vibration.
In closed tubes a quarter wavelength is the simplest wave form capable of creating a standing wave. Therefore, a quarter wavelength generates the fundamental frequency. As a result,
Substitute this into the equation for wave speed.
Substitute values and solve.
For tubes use the speed of sound in air, 343 m/s, unless the problem specifically states that the tube is in another medium.