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). node antinode Physical picture of particle motions (sound wave in a closed tube) graphical picture

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) node antinode graphical picture

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

L a) Pipe with both ends closed

L b) Pipe with both ends open

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

Beats Chap 18

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

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 wave. It has much longer wavelength and much slower frequency

time t in phase 180 o out of phase in phase

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 2A # 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 440Hz and another has a frequency 450Hz. 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