Doppler Effect

difference between the perceived frequency of a sound and its actual frequency when the source of the sound and the sound's detector are moving relative to each other

- If the source and detector are
each other, the**moving toward****perceived frequency f′ is greater than the actual frequency f**, - if the source and detector are
from each other, the**moving away****perceived frequency f′ is less than the actual frequency f.** **f'=f[(v +/-v**_{D})/ (v-/+ v_{s})*where v is the speed of sound in the medium, v*_{D}is the speed of the detector relative to the medium, and v_{S}is the speed of the source relative to the medium. The upper sign on v_{D}and v_{S}is used when the detector and the source are getting closer together. The lower sign is used when the detector and the source are going farther away from each other.

strings (standing waves)

*λ=(2L)/n*

*where n is a positive nonzero integer (n = 1, 2, 3,… )*

*Pattern: * etc.

From relationship that f=v/λ, the __ possible frequencies__ are:

**f=(nv)/2L**

where n is a positive nonzero integer (n = 1, 2, 3,… ).

open pipes

*λ=(2L)/n*

*where n is a positive nonzero integer (n = 1, 2, 3,… )*

*Pattern: * etc.

From relationship that f=v/λ, the __ possible frequencies__ are:

**f=(nv)/2L**

where n is a positive nonzero integer (n = 1, 2, 3,… ).

harmonic series

__ fundamental frequency( first harmonic)__: lowest frequency (longest wavelength) of a standing wave that can be supported in a given length of string

__ second harmonic:__ frequency of the standing wave given by n = 2 is known as the firstovertone or This standing wave has one-half the wavelength and twice the frequency of the first harmonic. All the possible frequencies that the string can support form its harmonic series.

*The waveforms of the first three harmonics for a string of length L are shown.(Note: N stands for node and A stands for antinode.)*

Closed Pipes

**λ=4L/n**

where n is odd integers only (n = 1, 3, 5,… ). The frequency of the standing wave in a closed pipe is *f=nv/4L*