Chapter 21: Superposition and standing wave

1. Chapter 21: Superposition and standing wave The principle of Superposition: When two or more waves are simultaneously present at a single point in space, the displacement of the medium at that point is the sum of the displacements due to each individual wave.

2. Stop to think 21.1 page 648Stop to think 21.2 page 654Stop to think 21.3 page 658 • Example 21.1 page 651 • Example 21.2 page 654 • Example 21.5 page 656 • Example 21.6 page 658

3. Standing wave Ex: there are two waves: The resultant wave function is: Notice, in this function, does not contain a function of (kx±ωt). So it is not an expression for a traveling wave

4. Standing wave on a String • A standing wave can exist on the string only if its wavelength is one of the values given by • F1=V/2L fundamental frequency. • The higher-frequency standing waves are called harmonics, ex. m = 2, second harmonics m=3 third harmonics Node Antinode

5. Stop to think: A standing wave on a string vibrates as shown at the figure. Suppose the tension is quadrupled while the frequency and the length of the string are held constant. which standing-wave pattern is produced Answer: a

6. Standing Sound Waves • Open-open or closed-closed tube m =1,2,3……

7. Open-closed tube

8. Problem 21.54 • Model: A stretched wire, which is fixed at both ends, creates a standing wave whose fundamental frequency is f1 = V(wire)/2L. A standing wave in an open-closed tube exhibits an antinode at the open end and a node at the closed end.

9. =469 Hz The nodes of standing wave are spaced λ/2, it is 36 cm, so the λ = 72 cm The v = 469/s x 0.72 m = 338m/s. It is closed to 343m/s, the speed of sound at 20 C

10. Interference in one dimension • The phase: • The phase difference is • Constructive interference: ΔΦ = m(2π) • Perfect destructive interference ΔΦ = (2m + 1 )π