11.2. Wave Speed http://www.ck12.org
Illustrative Example 1
a. The ripple tank arm inFigure11.9 has a period of 0.25 s and the length of the arrow in the figure is 3.76 cm.
What is the wavelength of the water waves if the picture is to scale?
FIGURE 11.9
Answer:There are four wavelengths from the start to the end of the arrow. Wavelength is:λ=^3 .76cm 4 = 0 .94cm
b. What is the velocity of the wave?
Answer:
Since the period isT= 0 .25 s, the frequency is, f=T^1 = 0 .25 s^1 = 4 .0 Hz or four cycles per second.Sothe velocity
isv=λf= ( 0 .94 cm)( 4 .0 Hz) = 3. 76 cms.
Check Your Understanding
- A sound wave travels at the speed of 343.0 m/s through the air at room temperature, 20. 0 ◦C( 68. 0 ◦F). If the
frequency of the sound is 261.6 Hz (a middle-C note), what is the wavelength of the note?
Answer:v=λf→λ=vf=^343261 ..0 m/s6 Hz= 1 .311 m
- X-rays are electromagnetic waves. A particular type of x-ray has a frequency of 3. 0 × 1017 Hz and a wavelength
of 1. 0 × 10 −^9 m. What is the velocity of this type of x-ray?
Answer:v=λf=
(
- 0 × 10 −^9 m)( 3. 0 × (^10171) s
)
= 3. 0 × 108 m/sThis result is true for any electromagnetic radiation traveling in a vacuum, including visible light.
- Compared to the speed of sound in air at a temperature of 20◦C, how many times faster is the speed of light
through the air at the same temperature?
Answer:We’ll assume that the velocity of lightvL= 3. 0 × 108 ms is approximately the same through the air as it is