Today s Topic: Beats & Standing Waves

Transcription

1 Today s Topic: Beats & Standing Waves Learning Goal: SWBAT explain how interference can be caused by frequencies and reflections. Students produce waves on a long slinky. They oscillate the slinky such that it generates 5 crests every 2 seconds. If the crests travel down the hallway at a rate of 1.5 m/s, what is crest-to-trough distance of these waves?

2 Due Today, 6/3: Homework Complete the Wave Speed Worksheet Due Tuesday, 6/9: Complete the Wave Interference Worksheet Three Days Late: Pendulum Lab Simple Harmonic Motion Worksheet

3 Recap What is wave superposition? What are the three possible outcomes for when waves interfere/superimpose onto each other? Constructive Interference Destructive Interference Complete Destructive Interference

4 Wave Interference Let s the visualization of waves again residing in the same place at the same time. What is happening at the spokes? What is happening between the spokes?

5 Other Types of Interference We just studied one type of interference pattern where amplitudes are affected. However, frequencies can also produce a type of interference as well. What does the frequency of a wave tell you about the wave? What does frequency affect when dealing with sound?

6 Frequency-based Interference Let s say we have two waves: What do we notice about these waves

7 Frequency-based Interference If we superimpose these waves We would find areas of constructive and destructive interference. What does the amplitude of a sound wave affect? Volume!

8 Beats by Physics If we listened to this, we would hear something strange (Video)

9 Beats What we heard are an example of beats! When two waves of slightly different frequencies interfere, the interference pattern varies in such a way that a listener hears an alternation between loudness and softness. The variation from soft to loud and back to soft is called a beat.

10 Beat Frequencies This happens due to the difference in frequencies of your sounds.

11 Beat Frequencies The smaller the difference, the more noticeable it is. We can see a better example here. (3:00) If you take the difference in frequencies of your sounds, you will find the beat frequency: f beat = f 1 f 2

12 Beat Examples A frequency generator makes a tone of 200 Hz. A second frequency generator makes another tone of 203 Hz. What is the beat frequency of these tones?

13 Beat Examples Two musicians are each playing one note on a clarinet. The first musician plays a note with wavelength m and the second plays a note with a wavelength of m. What are the frequencies of the notes they are playing? What is the beat frequency they are producing? Will they actually hear a beat?

14 Beat Examples A piano tuner using a 512 Hz tuning fork to tune the wire for C hears 4 beats per second. What are the two possible frequencies of vibration of this piano wire?

15 Waves at Boundaries We ve seen what happens when waves interact with other waves. We ve also studied what happens when waves travel indefinitely outwards. But what happens when waves interact with their surroundings and physical boundaries? For this, we need our Slinky again and two volunteers.

16 Waves at Boundaries Using the Slinky, I want you to create a wave pulse and observe what happens to the wave when it comes back. What do you notice about the wave that returns? Why does this happen? How is the person at the other end holding their hand?

17 Waves at Boundaries What does Newton s 3 rd Law say? For every action, there is an equal and opposite reaction. When the pulse reaches the person s hand, (or a fixed object), the Slinky exerts an upwards force on the hand.

18 Waves at Boundaries The wall, in response to this force, provides and equal and opposite reaction force on the Slinky. This downward force on the Slinky causes a displacement in the opposite direction from the original pulse. As a result, the pulse is inversed after reflection.

19 Reflection When a wave reaches a boundary between two media, usually some or all of the wave bounces back into the first medium. The return of a wave back into its original medium is called reflection.

20 Reflection Types For now, there are two types of boundaries that we are going to examine: Rigid (fixed) boundaries Free boundaries At a fixed boundary, waves are reflected and inverted.

21 Reflection Types This can also be seen using our Wave on a String Demo. But let s only focus on what happens to a wave at a rigid (fixed) boundary.

22 More Interference If we send one wave down the Slinky, it will head back. What if we send another pulse down the Slinky? And again? And again?

23 Standing Waves If you time it just right, you can generate a standing wave. A standing wave is wave that appears to stay in one place; it does not seem to move through the medium.

24 Standing Waves Standing waves are created by alternating regions of constructive and destructive interference.

25 Standing Waves What happens if we shake the Slinky slower? How many wavelengths do you see? One half of one wave length! This is known as the fundamental frequency.

26 Standing Waves An object s fundamental frequency (or first harmonic, or natural frequency) is the harmonic with the longest wavelength and lowest frequency. What if we shake the Slinky faster? How many wavelengths do we see? This is the second harmonic.

27 Standing Waves What if we shake the Slinky faster? How many wavelengths do we see? This is the third harmonic. To make more harmonics, frequency must increase. How can we describe this motion? What are those areas where the Slinky doesn t seen to move?

28 Standing Wave Terminology Nodes are the stationary points on a standing wave.