Waves at Boundaries – 8.2

What does the speed of a wave depend on? The speed of a wave does not depend on the amplitude or frequency. The speed of a wave depends on the properties of the medium in which it travels. THIS IS A PROPERTY OF THE MEDIUM NOT THE WAVE (LIKE BOILING POINT, DENSITY, ETC)

Examples Solids, liquids and gases are different mediums. The medium with the slowest waves would be solids! WHY? Solids have molecules that are tightly packed. This is why sound is distorted in water – the sound waves travel slower!

What does the speed of a wave depend on? The forces between the particles of the medium (the greater the force between the particles, the FASTER the wave moves) The mass of the particles of the medium (the greater the mass/inertia of the particles, the SLOWER the wave moves)

Although a wave with a larger amplitude transfers more energy, it moves with the same speed as a smaller amplitude wave through a given medium. As long as the material is the same, the speed of high and low frequency waves is the same.

Quick Quiz 1. 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.

Answer Both arrive at the same time! Same material!

2. Which of the two pulses (C or D) will travel from the hand to the wall in the least amount of time ? Justify your answer.

Answer Neither! Both will have the same speed. Since they go the same distance they will arrive at the same time!

3. 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. a. one-ninth b. one-third c. the same as d. three times larger than

Answer C.

4. While hiking through a canyon, Noah Formula lets out a scream. An echo (reflection of the scream off a nearby canyon wall) is heard 0.82 seconds after the scream. The speed of the sound wave in air is 342 m/s. Calculate the distance from Noah to the nearby canyon wall.

Answer If it takes 0.82 s to travel to the canyon wall and back (a down-and-back time), then it takes 0.41 s to travel the one-way distance to the wall. Now use d = v t d = v t = (342 m/s) (0.41 s) = 140 m

5. The speed of a wave depends upon (i.e., is causally affected by)... a.the properties of the medium through which the wave travels b.the wavelength of the wave. c. the frequency of the wave. d. both the wavelength and the frequency of the wave.

Answer A

Wave Reflection and Transmission Occurs when the wave reaches the boundary of a medium. The boundary can be a new medium or “wall”. When a wave moves from one medium to another, its frequency remains the same but its speed changes.

Reflection and Transmission Imagine a spring that is larger at one end. The wave will travel slower at the larger end than at the smaller end. The large end is the slower medium. Imagine guitar strings. A pluck on the high notes creates a faster vibration because the medium (thin string) is a faster medium.

Animations of Waves at Boundaries Demos/reflect/reflect.html

Incident Wave Approaching wave - it strikes a boundary where it is either reflected (bounced back) or refracted (changes direction/angle). Part of the energy of the incident wave carries on to the new medium. This means some of the energy remains in the original medium.

Transmitted Wave Wave that is transmitted to the new medium.

Reflected Wave Wave that does not move to the new medium but backward from the boundary.

Diagram

Waves at Boundaries If the medium is similar, the amplitude of the transmitted wave will be almost as large as the incident wave. Most of the energy will be transmitted. If the medium is different, most of the wave energy will be reflected.

Wave Boundary – Less Dense to More Dense Medium The reflected wave is inverted. The denser medium has a smaller amplitude and wavelength (less energy). The frequency does not change.

Wave Boundary – Less Dense to More Dense Medium /waves/ltm.cfmhttp:// /waves/ltm.cfm

Wave Boundary – More Dense to Less Dense Medium The reflected wave is erect (not inverted). The less dense medium has a smaller amplitude (less energy). The frequency does not change.

Quick Quiz Case 1: 1. The reflected pulse in medium 1 ________ (will, will not) be inverted because _______. 2. The speed of the transmitted pulse will be ___________ (greater than, less than, the same as) the speed of the incident pulse. 3. The speed of the reflected pulse will be ______________ (greater than, less than, the same as) the speed of the incident pulse. 4. The frequency of the transmitted pulse will be ___________ (greater than, less than, the same as) the frequency of the incident pulse. 5. The amplitude of the transmitted pulse will be ____________ (greater than, less than, the same as) the frequency of the incident pulse.

Answers 1. will not... because the reflection occurs for a wave in a more dense medium heading towards a less dense medium. 2. greater than 3. the same as 4. the same as 5. less than

Quick Quiz Case 2: 1. The reflected pulse in medium 1 ________ (will, will not) be inverted because _______. 2. The speed of the transmitted pulse will be ___________ (greater than, less than, the same as) the speed of the incident pulse. 3. The speed of the reflected pulse will be ______________ (greater than, less than, the same as) the speed of the incident pulse. 4. The frequency of the transmitted pulse will be ___________ (greater than, less than, the same as) the frequency of the incident pulse. 5. The amplitude of the transmitted pulse will be ____________ (greater than, less than, the same as) the frequence of the incident pulse.

Answers 1. will... because the reflection occurs for a wave in a less dense medium heading towards a more dense medium. 2. less than 3. the same as 4. the same as 5. less than

Wall Boundaries When a spring is attached firmly to a wall, the reflected wave is inverted (like a fast to slow boundary). The reflected wave is much faster than the transmitted wave as the wall is denser. Let’s try it!

Waves with “Loose Ends” If a pulse travels down a spring not attached to anything, the reflected pulse will be erect, not inverted. The reflected pulse is identical to the incident pulse (like a slow to fast boundary). The air is the next medium.

Questions for You Can the transmitted pulse ever be inverted? NO!!! Can we always see a transmitted pulse? NO!!! Solid wall boundaries!

Answers 1. a) Trans wave is faster (less dense medium) but same frequency. Smaller amplitude for ref. Trans – smaller amplitude. Ref. wave – same speed. B) Reflected wave is erect not inverted. C) Reflected wave is same frequency and speed (same medium), smaller amp. Trans wave – smaller amp, smaller speed, same f. D) Reflected wave is inverted. a/b c/d

Answers 2. It is attached to the wall because the reflected wave is inverted.

Answers 3. Lower frequency – it will allow the wavelengths to be longer.

Answers 4. a) The medium for B is denser, so the boundary creates an inverted reflected wave. Some of the wave is reflected, some is transmitted. Transmitted wave is slower than incident wave. Ref. wave is same speed. B) inverted C) Reflected wave is same speed than incident wave. Trans wave is slower than incident wave. Same frequencies, smaller amps for both. D) inverted