Physics P Worksheet 14.2b Periodic Motion and Waves
Worksheet 14.2b Periodic Motion and Waves
Speed of sound in air = 340 m/s Speed of light = 2.9979 × 108 m/s 1. The crests of an ocean wave are 20 m apart and you measure one wave every 10 seconds (or the frequency
= 1/10 Hz). Find the speed of the wave. 2. Tides can be considered to be a big wave. The length of the wave is half the circumference of Earth (which
is 24000 miles around) and the period is 12 1/2 hours. What is the speed of this wave? 3. FM radio waves have frequencies ranging from 88.0 MHz up to 108.0 MHz. (1 MHz = 1 × 106 Hz)
Determine the wavelengths of the waves in this range. 4. AM radio waves have frequencies ranging from 550 kHz up to 1600 kHz. (1 kHz = 1 × 103 Hz) Determine
the wavelengths of the waves in this range. 5. Humans can hear sounds ranging from 20 Hz up to 20 kHz. Determine the wavelengths of the waves in this
range. 6. The human eye can detect waves ranging from 450 nm to 650 nm. (1 nm = 1 × 10-9 m). Determine the
frequencies of the waves in this range. 7. A radio antenna works best if its length is exactly one quarter of a wavelength of the wave being received.
What is the optimum length for an FM radio antenna? (Use what you did in #3) 8. Water waves in a shallow dish are 6.0–cm long. At one point, the water moves up and down at a rate of 4.0
oscillations/s. What is the speed of the water waves? 9. What is the period of a pendulum with a length of 1.4 m? 10. The speed at grandfather clock is controlled by a swinging pendulum. If the pendulum is currently 15.0 cm
in length, by how much should the length be changed to shorten the period by 0.0400 s? 11. When you add a 45–kg load to the trunk of a car, the two rear springs compress an additional 1.0 cm. What
is the spring constant of each of the springs? 12. The Sears tower in Chicago sways back and forth with a frequency of 0.12 Hz. What is its period of
oscillation? 13. An ocean wave has a length of 12 m and a wave passes a point every 3 s. What is the speed of the waves? 14. The speed of sound in water is 1498 m/s. A sonar signal is sent from a ship straight down to the bottom of
the ocean and the echo returns 1.8 s later. How deep is the water. 15. The velocity of longitudinal waves in an earthquake is 8.9 km/s and the speed of transverse waves in an
earthquake is 5.1 km/s. A seismograph records the arrival time of the longitudinal wave 68 s before the arrival of the transverse wave. How far away is the earthquake?
Physics P Worksheet 14.2b Periodic Motion and Waves 1. 𝑣 = !
!
𝑣 =20 m10 s
𝑣 = 2 ms
2. 𝑣 = !
!
𝑣 =12 000 mi12.5 h
𝑣 = 960 mih
3. 𝑣 = 𝑓𝜆
𝜆 =𝑣𝑓
𝜆 =3 ×108 ms88 ×106 Hz
𝜆 = 3.41 m 𝑣 = 𝑓𝜆 𝜆 =
𝑣𝑓
𝜆 =3 ×108 ms
108 ×106 Hz
𝜆 = 2.78 m
4. 𝑣 = 𝑓𝜆 𝜆 =
𝑣𝑓
𝜆 =3 ×108 ms
550 ×103 Hz
𝜆 = 545 m 𝑣 = 𝑓𝜆 𝜆 =
𝑣𝑓
𝜆 =3 ×108 ms
1600 ×103 Hz
𝜆 = 188 m
5. 𝑣 = 𝑓𝜆 𝜆 =
𝑣𝑓
𝜆 =𝑣𝑓
𝜆 =340 ms20 Hz
𝜆 = 17 m
𝑣 = 𝑓𝜆 𝜆 =
𝑣𝑓
𝜆 =340 ms
20 ×103 Hz
𝜆 = 0.017 m
6. 𝑣 = 𝑓𝜆 𝑓 =
𝑣𝜆
𝑓 =3 ×108 ms
450 ×10-‐9 m
𝑓 = 6.67×10!" Hz
𝑣 = 𝑓𝜆 𝑓 =
𝑣𝜆
𝑓 =3 ×108 ms
650 ×10-‐9 m
𝑓 = 4.62×10!" Hz
7. Assume as average wavelength of 3 m. 𝐿 = !
!𝜆 𝐿 = !
! 3 m 𝐿 = 0.75 m
8. 𝑣 = 𝑓𝜆 𝑣 = 4.0 Hz 0.060 m 𝑣 = 0.24 ms
9. 𝑇 = 2𝜋 !!
𝑇 = 2𝜋1.4 m9.8 !!!
𝑇 = 2.4 s
Physics P Worksheet 14.2b Periodic Motion and Waves
10. 𝑇 = 2𝜋 !!
𝑇 = 2𝜋0.15 m9.8 !!!
𝑇 = 0.7773 s 0.7773 s – 0.0400 s = 0.7373 s
𝑇 = 2𝜋𝑙𝑔
𝑙 =𝑔𝑇!
4𝜋!
𝑙 =𝑔 0.7373 s !
4𝜋!
𝑙 = 0.135 m Δ𝑙 = 0.15 m-‐0.135m Δl = 0.015m
11. 𝐹 = 𝑘𝑥
𝑘 =𝐹𝑥
𝑘 =𝑚𝑔𝑥
𝑘 =45 kg 𝑔0.01 m
𝑘 = 44 100 Nm
12. 𝑇 = !
!
𝑇 =1
0.12 Hz
𝑇 = 8.3 s
13. 𝑣 = !!
𝑣 =12 m3 s
𝑣 = 4 ms
14. 𝑣 = !!
!!
Δ𝑑 = 𝑣Δ𝑡 Δd = 1498 ms 1.8 s Δd = 2696 m depth = 1348 m
15. 𝑡! − 𝑡! = 68 s Δ𝑑𝑣!
−Δ𝑑𝑣!
= 68 s
Δ𝑑5100 ms
−Δ𝑑
8900 ms= 68 s
8900Δ𝑑8900 5100 !!
−5100Δ𝑑
5100 8900 !!= 68 s
8900 − 5100 Δ𝑑 = 5100 8900 !! 68 s
Δ𝑑 =5100 8900 !! 68 s8900 − 5100
Δ𝑑 = 812000 m