WAVES BEATS: INTERFERENCE IN TIME

Transcription

1 VISUAL PHYSICS ONLINE WAVES BEATS: INTERFERENCE IN TIME Beats is an example o the intererence o two waves in the time domain. Loud-sot-loud modulations o intensity are produced when waves o slightly dierent requencies are superimposed. Consider two sound sources producing audible sinusoidal waves at slightly dierent requencies and 2. How can a piano tuner use s in tuning a piano? What will the person hear? I the two waves at irst are in phase they will interere constructively and a large amplitude resultant wave occurs which will give a loud sound.

2 As time passes, the two waves become progressively out o phase until they interere destructively and the sound will be very quiet. The waves then gradually become in phase again and the pattern repeats itsel. Figure () shows a resultant waveorm with rapid luctuations but with an envelope that various slowly. Fig.. Beat pattern. Two waves with dierent requency create a because o intererence between them. The requency is the dierence o the two requencies. Estimate, 2 and. 2

3 The requency o the rapid luctuations is the average requency o and The requency envelope o the slowly varying envelope is given by hal the absolute value o the dierence in the requencies and 2 envelope 2 2 Since the envelope has two extreme values in a cycle, we hear a loud sound twice in one cycle since the ear is sensitive to the square o the wave amplitude. This is called the requency requency 2 3

4 Example 000 Hz 2 00 Hz Rapid oscillations Hz 005 Hz 2 2 T x0 s = ms Beats Hz 0 Hz 0.0 s T 0.0 s loud pulsation will be heard every 4

5 Example Hz Hz Rapid oscillations Hz 00 Hz 2 2 T x0 s = ms Beats Hz 20 Hz T s s loud pulsation will be heard every 5

6 Example Hz Hz Rapid oscillations Hz 025 Hz 2 2 T x0 s = ms Beats Hz 50 Hz T s s loud pulsation will be heard every 6

7 Exercise From the graphs shown in exercises 2, 3 and 4 veriy the numerical results given in the three Examples. Beats can occur with any kind o wave and the best example is with sound waves. A piano tuner listens or s produced rom a standard requency and the string to be tuned. The string is tuned when the two strings have the same requency and the s disappear. The detection o relative motion by dolphins is explained using the Doppler Eect and s. The dolphin sends out a signal and detects any echoes. I there is zero relative motion, then the two signals have the same requency and no s are detected. I there is relative motion, then one or both o the signals will have a change in requency due to the Doppler Eect and so the two requencies will be slightly dierent and s will be detected. 7

8 The same principle is used by the polices radar units to catch you speeding. Bats emit a 'chirp', and listen to the echoes. From these echoes bats can build a rich picture o the world about them just as dolphins can detect relative motion. You hear dolphins call, but you can't hear bats. Why not? Humans can only hear sound up to about 6 khz. Bats emit sounds at typically 2 or 3 times higher pitch than we can hear. Sounds above human hearing are usually called ultrasonic. Whales and elephants can make sounds below what we can hear, about 6 Hz and these are called inrasonic. Plucking two guitar strings o slightly dierent requencies will produce s. The members o an orchestra can tune up by listening or s between their instruments and that o a standard tone, usually A above middle C at 440 Hz produced by a piano or an oboe. Two piano strings diering in requency by about 3 Hz sounds out o tune. 8

9 The phenomena o Doppler Eects and Beats is used in the images o the blood low through the heart are captured using ultrasound. Web search: Cardiovascular and Doppler ultrasound. 9

10 The engines o multiengine propeller planes have to be synchronised so that the propeller sound does not produce annoying s which would be heard as a loud throbbing sound. 0

11 Example A tuning ork produces a steady note at 440 Hz tone. When this tuning ork is struck, and held near a vibrating guitar string, 20 s are counted in 5.0 seconds. What are the possible requencies produced by the guitar string? Solution Tuning ork 440 Hz Guitar 2? Hz Beat requency 20 / 5 Hz 2 Guitar Hz or Hz

12 Beats between two sounds can be heard up to about 7 Hz. For requency greater than about 7 Hz, we no longer hear individual s and the sensation merges into one o consonance or dissonance depending on the ratio o the two requencies. In music, consonance and dissonance are categorizations o simultaneous or successive sounds. Consonance is associated with sweetness, pleasantness, and acceptability. Dissonance is associated with harshness, unpleasantness, or unacceptability. EXCEL SIMULATION: Download the MS EXCEL spreadsheet BEATS.XLS VISUAL PHYSICS ONLINE I you have any eedback, comments, suggestions or corrections please Ian Cooper School o Physics University o Sydney ian.cooper@sydney.edu.au 2