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## wave mechanics

### (4 points)3. Series 26. Year - 4. Supersonic or subsonic?

Imagine a bomb that is free-falling on a military base of your enemies. Although you threw the bomb off an airplane, you should assume that its motion is vertical (i.e. no horizontal component of its velocity relative to the surface). Because of air friction, the falling bomb emits a sound that propagates at the speed c = 340 m/s. What is the maximal impact velocity of the bomb in order for your enemies to hear it before it kills them?

Lukas was staring at ducks on a lake.

### 5. Series 24. Year - E. chordates

Create an apparatus that will enable you to fix a string of variable length in such a way that the tension in the string is the same for all lengths. Find the relationship between the main frequency of the string and its length. To process the sound you may use some software like Audacity.

Karel

### 2. Series 24. Year - E. Yin and young

Most of you have probably heard about the Young's double slit experiment. Have you, however, ever tried to reproduce this experiment and see the interference patterns for yourselves? There are also mechanical analogies to this experiment. For example you can observe the interference of two waves in water or two sound waves. Choose one or more of these experiments and measure the interference pattern. Then you can calculate the wave length and the speed of wave propagation. Photos of your apparatus will be welcomed!

eee

### 2. Series 24. Year - P. The Smurfs and Darth Vader

If you inhale some helium your voice changes so that you speak like a smurf. Hydrogen has the same effect (watch out smokers!) but it is also possible to obtain the voice of Darth Vader in this way. The most famous substance for this is sulfur hexafluoride. What causes the voice to change? Make also a quantitative guess.

eee

### 5. Series 23. Year - E. resonance

When you stand in an enclosed space and play a right tone, you can face its resonance frequency. As the resonance frequency depends on the size of the resonator, it can thence be determined. Choose an appropriate room (ideally, a small one with empty walls – e.g. bathroom), measure the frequency and contrast the results.

sang in the bathroom by Jakub Michálek

### 6. Series 22. Year - E. returnable flasks

Buy a standard glass bottle from bier of mineral water and find out, how the pitch of the tone depends on the water level inside the bottle, when you blow over the neck of the bottle.

vymysleli organizátoři na pravidelné schůzi

### 5. Series 22. Year - P. noise

Estimate, what energy is absorbed by the body of visitor on a rock concert. Give reasons for your answer.

na schůzku donesl Honza Jelínek

### 2. Series 22. Year - 4. into infinity and even further

An rich space-tourist has payed for a trip to the deep space. The Racket flies from the Earth and is accelerating with constant acceleration $a$, which can be verified by dropping a small ball. He is quite bored and therefore is watching disappearing Earth through the back window. After some time (how long it will take?) he starts to see, that something is not right. The Earth is not getting much smaller, and he deduces, that the space ship is slowing down, which does not correspond with the constant acceleration of $a$. However the tourist is not as good physicist and goes to file complain with captain. What should the captain to tell him?

Assume, that the tourist see whole electromagnetic spectrum and will survive the observation.

o prázdninách zkoušel Marek Pechal

### 2. Series 22. Year - S. Young and wave character of light

• What shape of interference pattern would you expect in following two configurations? Find the equations of curves of maximum intensity and try to plot some of them.
• Show, how the experiment should end, if the light behaves according to Newton assumptions. Do consider different angle of incidence at different places on the screen.
• Using quantum-mechanical description find resolution, which should have get Jöhnsson by using 4 slits (4 parallel orifices in distance $b$ between neighbouring slits. Plot representative part of the graph and comment advantages of higher number of orifices.

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