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