1. Waves II Sound waves, Free and forced vibrations, Resonance, Standing waves (strings, open & closed pipes) & Beats

2. Sound Wave Sound is a wave. (Musical laser and Oscilloscope set up) Sound waves are longitudinal waves produced due to vibrations that causes pressure changes. (Wave machine) Speed of sound is the fastest in solids and slowest in gases. (Hanger Banger)

3. Sound Wave Speed of sound depends on temperature. Speed of sound in air is about 332m/s at 0°C. It increases 0.6m/s for each Celsiusº above zero. (Lab) For problem solving in our class, we will assume the speed of sound to be 340m/s. Human frequency range is 20Hz to 20KHz (20Hz – 20,000Hz)

4. Free and forced vibrations When an object is tapped, it will vibrate with its own natural frequency. This is free vibrations. (This is why different objects sound different when tapped.) When there is vibrations around an object and it is forced to pick up that particular vibration, it is called forced vibrations.

5. Resonance When the forced vibrations happens to be the same as the natural frequency of the object, the object happily picks up the energy and starts to oscillate. This is called RESONANCE. Examples of resonance are swings, Tacoma bridge collapse, breaking wine glasses.

6. Standing waves in Strings When waves are continuously sent (incident waves); and they hit a rigid boundary (reflected wave) then, they come back out of phase. These incident and reflected waves interact to form standing waves as shown.

7. Standing waves in Strings - The faster the vibrations, the more the nodes and antinodes. - Observe that the nodes are at the fixed ends (for strings only). - The greater the frequency, the smaller the wavelength. - n=1, tell me that there is one anti-node (fundamental frequency).

8. Standing waves in Strings Knowing the length, the actual wavelength of the standing wave can be calculated. 1 st Harmonic is also called fundamental frequency.

9. Standing waves in Strings Knowing the wavelength and the speed of the waves, its fundamental frequency (1 st harmonic) and the other harmonics (2 nd, 3 rd, etc) can be calculated. n=1 (1 st harmonic) n=2 (2 nd harmonic) n=3 (3 rd harmonic)… These harmonics are also called overtones or octaves.

10. Standing waves in Strings Using, V=f λ f = V/ λ = V/[2L/n] = nV/2L Here n is the # of harmonic, V is the speed of the wave, L is the length of the wave and f is the frequency of that particular harmonic.

11. Standing waves in Strings Over all, we can see that since the medium (string) is the same, changing wavelength results in changing frequency! Just like we saw in the slinky lab! If the wavelength halves, the frequency doubles. So we can say that: f 1 : f 2 : f 3 : f 4 = 1: 2: 3: 4

12. Standing Waves in Open Pipes Definition : Open pipes are open at both ends. Examples are straws, etc. You can blow into straws and create a loud sound. This can only be done when blown with some particular frequency. These particular frequencies are capable of producing standing waves in open pipes.

13. Standing Waves in Open Pipes Observe that there are Anti-nodes at the open ends. This is because at the open ends, there is more room for air to vibrate and it prefers That.

14. Standing Waves in Open Pipes The wavelength can be calculated as shown. As in a string, f = V/ λ = V/[2L/n] = nV/2L

15. Standing Waves in Open Pipes Over all, we can see that since the medium (air column) is the same, changing wavelength results in changing frequency! Just like we saw in the slinky lab! If the wavelength halves, the frequency doubles. So we can say that: f 1 : f 2 : f 3 : f 4 = 1: 2: 3: 4

16. Standing Waves in Closed Pipes Definition : Closed pipes are closed at one end. Examples are pen caps, etc. You can blow into pen caps to create loud sound. These can only be done when blown with some particular frequency. These particular frequencies are capable of producing standing waves in closed pipes.

17. Standing Waves in Closed Pipes Observe that there are anti-nodes at the open end and nodes at the closed ends.

18. Standing Waves in closed Pipes The wavelength can be calculated as shown. f = V/ λ = V/[2L/n] = n’V/2L Here n’ is an odd number only. No even harmonics exist for closed tubes.

19. Standing Waves in closed Pipes Over all, we can see that since the medium (air column) is the same, changing wavelength results in changing frequency! Just like we saw in the slinky lab! Here however, we see that wavelength decreases in the 1: 3: 5: 7 ratio. And so we can say that: f 1 : f 3 : f 5 : f 7 = 1: 3: 5: 7 Even harmonics do not exist in closed pipes.

20. Beats Beats are superposition of very close frequency waves. See example below.

21. Beats The number of beats heard depends on the difference between the frequencies. # of beats = |f 2 – f 1 | In the above slide example, First wave frequency = 10Hz Second wave frequency = 12Hz So, # of beats = |f 2 – f 1 | = |12 – 10| = 2Hz

22. Beats Example: