Standing sound waves Standing sound waves Sound in

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Standing sound waves

Standing sound waves

Standing sound waves Sound in fluids is a wave composed of longitudinal vibrations of

Standing sound waves Sound in fluids is a wave composed of longitudinal vibrations of molecules. The speed of sound in a gas depends on the temperature. For air at room temperature, the speed of sound is about 340 m/s. At a solid boundary, the vibration amplitude must be zero (a standing wave node). Physical picture of particle motions (sound wave in a closed tube) node antinode graphical picture

Standing sound waves in tubes – Boundary Conditions -there is a node at a

Standing sound waves in tubes – Boundary Conditions -there is a node at a closed end -less obviously, there is an antinode at an open end (this is only approximately true) antinode graphical picture

Exercise: Sketch the first three standing-wave patterns for a pipe of length L, and

Exercise: Sketch the first three standing-wave patterns for a pipe of length L, and find the wavelengths and frequencies if: a) both ends are closed b) both ends are open c) one end open

a) Pipe with both ends closed L

a) Pipe with both ends closed L

b) Pipe with both ends open L

b) Pipe with both ends open L

c) Pipe with one closed end, one open end L

c) Pipe with one closed end, one open end L

Example: An organ pipe has a length of 1. 23 m and is open

Example: An organ pipe has a length of 1. 23 m and is open at one end. Find the frequencies of the first three harmonics (v=344 m/s).

Example: If an organ pipe is to resonate at 20 Hz, what is its

Example: If an organ pipe is to resonate at 20 Hz, what is its required length if: a) it is open at both end? b) it is open at one end?

Beats Chap 18

Beats Chap 18

Given two nearly identical harmonic waves with slightly different frequencies and wave numbers but

Given two nearly identical harmonic waves with slightly different frequencies and wave numbers but moving in the same direction. This is the product of two traveling waves.

Define : and

Define : and

For waves on a string, In this case the group and wave velocities are

For waves on a string, In this case the group and wave velocities are the same.

Nearly same as initial wave Much different than initial wave. This is the GROUP

Nearly same as initial wave Much different than initial wave. This is the GROUP wave. It has much longer wavelength and much slower frequency

time in phase 180 o out of phase in phase t

time in phase 180 o out of phase in phase t

Temporal Beats Two waves of different frequencies traveling in the same direction produce a

Temporal Beats Two waves of different frequencies traveling in the same direction produce a fluctuation in amplitude. Since the frequencies are different, the two vibrations drift in and out of phase with each other, causing the total amplitude to vary with time. y time 1 beat

Note: maximum intensity when “amplitude” part is 2 A # beats/second = beat frequency

Note: maximum intensity when “amplitude” part is 2 A # beats/second = beat frequency = twice the group frequency The beat frequency (number of beats per second) is equal to the difference between the frequencies. The frequency of the combined waves is:

Quiz: One tuning fork has a frequency 440 Hz and another has a frequency

Quiz: One tuning fork has a frequency 440 Hz and another has a frequency 450 Hz. a) What is the beat frequency of the sound heard with both tuning forks vibrating? A) 890 Hz B) 445 Hz C) 10 Hz D) 5 Hz What is the actual sound frequency heard in this case?

Spatial beats

Spatial beats