Unit 9 WAVES

What do you need to know about waves? 7.1 Understand that waves transfer energy without transferring matter 7.2 Describe what is meant by wave motion as illustrated by vibration in ropes and springs and by experiments using water waves. 7.5 Distinguish between transverse and longitudinal waves and give suitable examples. 7.3 Define the terms: speed (velocity), frequency, wavelength and amplitude. 7.4 Recall and use the equation v = f λ

7.1 Understand that waves transfer energy without transferring matter: wave motion Watch the Wave! A wave is, in general, a disturbance that moves through a medium. A wave carries energy from one location to another without transporting the material of the medium. Waves include mechanical waves (e.g. water waves, waves on a string, and sound waves) and non-mechanical waves (e.g. light waves)

Mechanical waves Mechanical waves are waves that can travel through a medium Mechanical waves are created when particles change their position so that they bump into other particles, which moves energy from one spot to another The energy is passed along in the form of movement from particle to particle, but the particles them selves don’t get passed along There are 2 types of mechanical waves: transverse and longitudinal

7.5 Distinguish between transverse and longitudinal mechanical waves and give suitable examples. There are two types of mechanical waves: Transverse waves: The particles of the medium vibrate up and down (perpendicular to the wave).

Longitudinal waves: The particles in the medium vibrate along the same direction as the wave (parallel). The medium undergoes a series of expansions and compressions. The expansions (rarefactions) are when the coils are far apart and compressions are when they are when the coil is close together. Compressions and expansions are the analogs of the crests and troughs of a transverse wave.

Light waves are also considered as transverse waves (we’ll consider that later)

7.5 Distinguish between transverse and longitudinal waves and give suitable examples. Vocabulary Definition Example Transverse waves Particle displacement is 90 degrees to the direction of travel. light Longitudinal waves Particle displacement is parallel to direction of travel Sound

7.3 Define the terms: speed (velocity), frequency, wavelength and amplitude. 7.4 Recall and use the equation v = f λ

Amplitude: maximum displacement from equilibrium Crest: Top part of the wave Trough: Bottom part of the wave Wavelength: Length from crest to crest or trough to trough

7.4 Recall and use the equation v = f λ Wave velocity v is the velocity with which the wave crest is propagating (moving). A wave crest travels one wavelength ( λ ) in one (time) period: v = velocity (m/s) = wavelength (m) T= period (s) f = frequency (Hz) The speed of a mechanical wave is constant in a given medium. The amplitude of a wave does not affect its wavelength, frequency or speed.

= 1/T a. Amplitude: maximum displacement from equilibrium A = 0.75 cm 1 For the motion shown in the figure, find: a. Amplitude b. Period c. Frequency a. Amplitude: maximum displacement from equilibrium A = 0.75 cm b. T = time for one complete cycle or wave T = 0.60 - 0.40 = 0.2 s c. f = # of complete waves in one second = 1/T = 1/0.2 = 5 Hz

2 Transverse waves traveling along a rope have a frequency of 12 Hz and are 2.40 m long. What is the velocity of the waves? f = 12 Hz λ = 2.4 m v = f λ = 12 (2.4) = 28.8 m/s

3 Water waves in a small tank are 6. 0 cm long 3 Water waves in a small tank are 6.0 cm long. They pass a given point at the rate of 4.8 waves per second. a. What is the speed of the water waves? λ = 0.06 m f = 4.8 Hz v = f λ = (0.06) 4.8 = 0.29 m/s b. What is the period of the waves? T = 1/f = 1/4.8 = 0.2 s

4 Microwaves are electromagnetic waves that travel through space at a speed of 3x108 m/s. Most microwave ovens operate at a frequency of 2450x106 Hz. What is the period of these microwaves? v = 3x108 m/s f = 2450x106 Hz = 4x10-10 s b. How long is the wavelength of these microwaves? v = f λ = 0.122 m

5 A sound wave is directed toward a vertical cliff 680 m from the source. A reflected wave is detected 4 s after the wave is produced.a. What is the speed of sound in air? d = 680 m t = 4 s (reflected time) t = 4/2 = 2 s = 340 m/s

c. What is the period of the wave? b. The sound has a frequency of 500 Hz. What is its wavelength? f = 500 Hz v = 340 m/s v = f λ = 0.68 m c. What is the period of the wave? = 1/500 = 0.002 s

A teacher attaches a slinky to the wall and begins introducing pulses with different amplitudes. Which of the two pulses (A or B) below will travel from the hand to the wall in the least amount of time? Justify your answer.

They will reach the wall at the same time. Don’t be fooled! The amplitude of a wave does NOT have an effect on its velocity Velocity of waves is predominantly affected by the properties of the medium through which it travels

The teacher then begins introducing pulses with a different wavelength The teacher then begins introducing pulses with a different wavelength. Which of the two pulses (C or D) will travel from the hand to the wall in the least amount of time ?

They will reach the wall at the same time. Don’t be fooled! The amplitude of a wave does NOT have an effect on its velocity Velocity of waves is predominantly affected by the properties of the medium through which it travels

Answer #4: B GIVEN: v = 340 m/s, d = 20 m Find time Use v = d / t and rearrange to t = d / v Substitute and solve. 20/340 = 0.059s

Two waves are traveling through the same container of nitrogen gas Two waves are traveling through the same container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be ________ the speed of wave A. one-ninth one-third c. the same as d. three times larger than

Two waves are traveling through the same container of nitrogen gas Two waves are traveling through the same container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be ________ the speed of wave A. one-ninth one-third c. the same as d. three times larger than Answer #5 : C The medium is the same for both of these waves ("the same container of nitrogen gas"). Thus, the speed of the wave will be the same. Alterations in a property of a wave (such as wavelength) will not affect the speed of the wave. Two different waves travel with the same speed when present in the same medium.

Two boats are anchored 4 meters apart Two boats are anchored 4 meters apart. They bob up and down, returning to the same up position every 3 seconds. When one is up the other is down. There are never any wave crests between the boats. Calculate the speed of the waves. The diagram is helpful. The wavelength must be 8 meters (see diagram). The period is 3 seconds so the frequency is 1 / T or 0.333 Hz. Now use speed = f • wavelength Substituting and solving for v, you will get 2.67 m/s.