Waves

One exciting thing from waves is the musical instruments:

guitar



Quantities in Waves

Name Symbol Unit Type
speed of light in a vacuum c m/s, meters per second scalar
Frequency f Hz, hertz scalar
absolute index of refraction n No Unit scalar
Period T s, seconds scalar
velocity or speed v m/s scalar
Wavelength λ m, meters scalar
Angle measured from the Normal Line θ ° scalar
Angle of Incidence θi = θ1 ° scalar
Angle of Refraction θ2 ° scalar
index of refraction of the first substance n1 No Unit here. scalar
index of refraction of the second substance n2 No Unit here. scalar
Wavelength 1 λ1 m, meters scalar
Wavelength 2 λ2 m, meters scalar

Key Things to Know in Waves

Key Words in Modern Physics

antinode, frequency, amplitude, period, wavelength, pitch, loudness, wavelength, standing wave, resonance, natural frequency

Formula in Waves

Example 1

a) Which characteristic of a light wave must remain the same as the light wave passes from glass into air?
(1) amplitude (3) period
(2) frequency (4) wavelength

Frequency of a wave remains the same as the wave travels from one substance into another substance.


b) Which characteristic of a light wave must increase as the light wave passes from glass into air?
(1) amplitude (3) period
(2) frequency (4) wavelength

Glass has a higher index of refraction n. Air has a lowest index of refraction. This can be seen from p.2 of the physics reference table. v = \( \frac{c}{n} \). Since air has a smaller n, therefore the speed of light in air vair is greater than vglass. The speed must be greater for light in air. Since v = f λ, and f remains the same as the light enters into air from glass, the wavelength λ of the light wave must be greater in air.

Example 2

A duck floating on a lake oscillates up and down 5.0 times during a 10.-second interval as a periodic wave passes by. What is the frequency of the duck’s oscillations?

Frequency of a wave = # of waves per second. = (# of waves) ÷ (time) = 5 waves ÷ 10 s = 0.5 Hz;
A wave = an oscillation up and down.

Example 3

The amplitude of a sound wave is most closely related to the sound’s
(1) speed (3) loudness
(2) wavelength (4) pitch

Loudness is our perception of a sound wave's amplitude.

Example 4

Wind blowing across suspended power lines may cause the power lines to vibrate at their natural frequency. This often produces audible sound waves. This phenomenon, often called an Aeolian harp, is an example of
(1) diffraction (3) refraction
(2) the Doppler effect (4) resonance

An object in resonance vibrates at its natural frequency.

Exercises

1. As a longitudinal wave moves through a medium, the particles of the medium
(1) vibrate parallel to the direction of the wave’s propagation
(2) vibrate perpendicular to the direction of the wave’s propagation
(3) are transferred in the direction of the wave’s motion, only
(4) are stationary

2. Compared to the wavelength of red light,
the wavelength of yellow light is
1) shorter
2) longer
3) the same

3. A gamma ray and a microwave traveling in a vacuum have the same
(1) frequency (3) speed
(2) period (4) wavelength

4. A student produces a wave in a long spring by vibrating its end. As the frequency of the vibration is doubled, the wavelength in the spring is
(1) quartered (3) unchanged
(2) halved (4) doubled

5. Which two points on the wave shown in the diagram below are in phase with each other?
Exercise 5 picture
(1) A and B (3) B and C
(2) A and E (4) B and D

6. A student listens to music from a speaker in an adjoining room, as represented in the diagram below.
Exercise 6 picture
She notices that she does not have to be directly in front of the doorway to hear the music. This spreading of sound waves beyond the doorway is an example of
(1) the Doppler effect (3) refraction
(2) resonance (4) diffraction

7. The horn of a moving vehicle produces a sound of constant frequency. Two stationary observers, A and C, and the vehicle’s driver, B, positioned as represented in the diagram below, hear the sound of the horn.
Exercise 7 picture
Compared to the frequency of the sound of the horn heard by driver B, the frequency heard by observer A is
(1) lower and the frequency heard by observer C is lower
(2) lower and the frequency heard by observer C is higher
(3) higher and the frequency heard by observer C is lower
(4) higher and the frequency heard by observer C is higher

8. The diagram below represents a ray of monochromatic light (f = 5.09 × 1014 Hz) passing from medium X (n = 1.46) into fused quartz.
Exercise 8 picture
Which path will the ray follow in the quartz?
(1) A (3) C
(2) B (4) D