1. Standing Waves Physics 11

2. Standing Waves When a wave travels in a medium of fixed length and is either forced at a specific frequency or most of the energy is reflected at the boundaries, a standing wave will result When a wave travels in a medium of fixed length and is either forced at a specific frequency or most of the energy is reflected at the boundaries, a standing wave will result A standing wave will result in a series of maxima and nodes depending on the medium A standing wave will result in a series of maxima and nodes depending on the medium

3. Fixed Both Ends Nodes at either end Nodes at either end 1 st harmonic is half a wavelength, with an anti-node (maxima) in the middle 1 st harmonic is half a wavelength, with an anti-node (maxima) in the middle 2 nd harmonic is one wavelength with a node in the middle and maxima between nodes 2 nd harmonic is one wavelength with a node in the middle and maxima between nodes

4. Fixed One End Generally “seen” in soundwaves Generally “seen” in soundwaves 1 st harmonic is one quarter of a wavelength with a node and maxima 1 st harmonic is one quarter of a wavelength with a node and maxima 2 nd harmonic is 3/4’s of a wavelength with two nodes and two maxima 2 nd harmonic is 3/4’s of a wavelength with two nodes and two maxima

5. Free Both Ends Similar to fixed both ends but nodes and maxima are reversed Similar to fixed both ends but nodes and maxima are reversed

6. Guitar String A guitar string has a given (open) length, given tension (and therefore mostly constant wave speed in a string) and therefore, when a string is plucked, a specific frequency is heard A guitar string has a given (open) length, given tension (and therefore mostly constant wave speed in a string) and therefore, when a string is plucked, a specific frequency is heard If the string is then shortened by a certain amount, a higher frequency can be played If the string is then shortened by a certain amount, a higher frequency can be played

7. Guitar String The low E string on a guitar has a fixed length of 67.5cm and plays a frequency of 82.41Hz; determine: The low E string on a guitar has a fixed length of 67.5cm and plays a frequency of 82.41Hz; determine: –The wavelength of the fundamental frequency (first mode of standing wave) –The wave speed

8. Guitar String The frets are placed at certain positions in order to allow specific notes to be played. If the next five notes are given by frequencies, 87.31Hz, 92.50Hz, 98.00Hz, 103.8Hz and 110.0Hz, determine: The frets are placed at certain positions in order to allow specific notes to be played. If the next five notes are given by frequencies, 87.31Hz, 92.50Hz, 98.00Hz, 103.8Hz and 110.0Hz, determine: –How long the string needs to be to play these notes –Where the frets should be placed

9. Questions Page 362 Page 362 –Questions 4-7