Chapter 19 Vibration and Waves
Exercises
4. Shorter pendulum has higher frequency and shorter period.
 | T =  |
| Shorter the Length shorter the Period (T). |
| Frequency = 1/Period Shorter Period higher Frequency. |
6. Period is less because standing raises the pendulum's center of mass.
16. Shake up and down for transverse. Push and pull on table for longitudinal.
17. (a) Transverse (b) Longitudinal (c) Transverse
21. Violet has the greater frequency.
| Longest wavelength has Lowest frequency (Red). |
| Shortest wavelength has Highest frequency (Violet). |
30. Wave speeds are the same in all radial directions.
31. Transverse wave of light travels 1 million times faster than longitudinal wave of sound.
| Lightning travels speed of light 300,000 km/s (3X108 m/s) |
| Thunder travels 340 m/s. |
32. Nodes are at the ends of the banjo string. Wavelength is 2X the length of the string. One wavelength needs one node between its ends.
33. Frequency doubles. f = v/λ same speed of sound but decrease wavelength 0.5 the frequency would double.
35. Doppler effect is change in frequency when move source, receiver, or both. Move towards and frequency increases. Move away and the frequency decreases.
36. (a) frequency increases (b) wavelength decreases (c) speed of sound is constant.
39. Doppler effect of radar waves (shift in frequency) bouncing off moving cars is used to calculate speeds.
40. Red shift - light lower frequency is moving away, and blue shift - light of higher frequency is moving towards. The shifts suggest the sun is spinning.
45. No. Sound is slower than the speed of light. See plane at its position in the sky then hear the delayed sound.
46. No. It follows on the ground as long as the speed is greater than the speed of sound.
48. Yes. The fish swimming faster than 1500 m/s in water would have a sonic boom.
Problems
1. (a) 10 Hz (b) .2 Hz (c) 60 Hz
2. (a) 0.1 s (b) 5 s (c) 1/60 s
3. P = 5 s and λ = 15 m
| f = 1/p = 1/5 = 0.2 vibs/s |
| v = λ * f = 15 m/vib * 0.2 vib/s = 3 m/s |
4. (a) f = 2 vibs/s = 2 Hz (b) P = 1/f = ½ = .5 s (c) amp = 10 cm
5. f = 100.1 MHz = 100,100,000 vibs/s; v = 300,000 km/s = 300,000,000 m/s
| λ = v/f = 300,000,000 m/s / 100,100,000 vibs/s = 3 m/vib |
6. λ = v/f = 340 m/s / 600 vibs/s = .567 m/vib
7. (a) Period = 1/f = 1/256 vibs/s = .0039 s (b) λ = v/f = 340 m/s / 256 vibs/s = 1.33 m/vib
8. (a) λ = v/f = 1500 m/s / 256 vibs/s = 5.86 m/vib It is longer. (b) Speed is faster, but frequency is the same. So to complete one period the wave travels farther in water than in air for the same time. The distance the wave travels in one period is longer in water.
9. TV λ = 3.42 m TV f = v/ λ = 300,000,000m/s / 3.42 m/vib = 87,719,298 vibs/s = 87.7 MHz This is below the Radio frequency of 88 - 108 MHz.
10. Sound goes from A to C and the plane goes from A to B. Angles are 45-45-90. Sides A-C equals side C-B. (A-B)2 = (A-C) 2 + (C-B) 2 = (1) 2 + (1) 2 = (2) 2
| Speed of plane = 1.41 X speed of sound = Mach 1.41 |
