Stosowanie zależności między okresem i częstotliwością oraz prędkością i długością fal w obliczeniach

Please prepare the answers to the following questions.

1. What is the vibrating motion?

2. Define the basic quantities describing the vibrating motion.

3. What is the mathematical pendulummathematical pendulummathematical pendulum?

4. What is the natural frequency?

5. Present on the graph the dependence between the displacement on time in the undamped harmonic motion and in the suppressed one.

6. Describe the mechanical energy changes which occur during the motion of the harmonic oscillator.

7. What is the mechanical wave? Describe the propagation of a mechanical wave.

8. Define the basic quantities describing the propagating wave.

9. Classify the waves according to the direction of wave propagationwave propagationwave propagation and the direction of vibrations.

10. What is the sound?

11. List and describe the properties of thesound.

12. What is echo and reverb?

13. What are ultrasoundsultrasoundsultrasounds and infrasounds?

Solve the test that revises the knowledge about vibrations and harmonic waves.

Exercise 5

The pendulums are placed on a common line.

Which one of them will start to vibrate, if we move pendulum No. 1?

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Na ilustracji narysowana jest pozioma linia, a do niej przyczepionych jest pięć wahadeł matematycznych, opisanych od lewej 1, 2, 3, 4 i 5. Wahadło matematyczne to punkt materialny zawieszony na nieważkiej i nierozciągliwej nici, której drugi koniec jest unieruchomiony. Linie pionowe, symbolizujące nici, są różnej długości i w równej odległości od siebie.

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Wersja alternatywna ćwiczenia: Możliwe odpowiedzi: 1. Pendulum No. 2, 2. Pendulum No. 3, 3. Pendulum No. 4, 4. Pendulum No. 5

Wersja alternatywna ćwiczenia: Możliwe odpowiedzi: 1. Pendulum No. 2, 2. Pendulum No. 3, 3. Pendulum No. 4, 4. Pendulum No. 5

• Pendulum No. 2
• Pendulum No. 3
• Pendulum No. 4
• Pendulum No. 5

Exercise 7

The period of the wave is 4 s, the amplitude is 1 m, half of the length is 2 m. What is its length and speed?

The period of the wave is 4 s, the amplitude is 1 m, half of the length is 2 m. What is its length and speed?

The period of the wave shown in figure is 4 s. What is its length, speed and amplitude?

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Na ilustracji narysowana jest pozioma linia. Od jej lewego końca krzywa (sinusoida). Zaznaczona odległość punktu na wykresie leżącego najdalej od linii poziomej - 1 m oraz odległość między dwoma punktami przecięcia wykresu z linią - 2 m.

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Wersja alternatywna ćwiczenia: Możliwe odpowiedzi: 1. $\lambda = 2 m, v = 2 \frac{m}{s}, A = 1 m$, 2. $\lambda = 2 m, v = 1 \frac{m}{s}, A = 2 m$, 3. $\lambda = 4 m, v = 1 \frac{m}{s}, A = 1 m$, 4. $\lambda = 4 m, v = 2 \frac{m}{s}, A = 2 m$

Wersja alternatywna ćwiczenia: Możliwe odpowiedzi: 1. $\lambda = 2 m, v = 2 \frac{m}{s}, A = 1 m$, 2. $\lambda = 2 m, v = 1 \frac{m}{s}, A = 2 m$, 3. $\lambda = 4 m, v = 1 \frac{m}{s}, A = 1 m$, 4. $\lambda = 4 m, v = 2 \frac{m}{s}, A = 2 m$

• $\lambda = 2 m, v = 2 \frac{m}{s}, A = 1 m$
• $\lambda = 2 m, v = 1 \frac{m}{s}, A = 2 m$
• $\lambda = 4 m, v = 1 \frac{m}{s}, A = 1 m$
• $\lambda = 4 m, v = 2 \frac{m}{s}, A = 2 m$

Summary

The wavelength (λ) is the distance between consecutive repetitions of the waveform. In other words, it is the smallest distance, measured parallel to the direction of the wavewave propagationwave propagation, between the points which are in the same vibration phase.

The wavelength is most easily determined by giving the distance between two consecutive wave crests or between its consecutive troughs.

For a wave spreading at the velocity v its length can be expressed:

The wave moving at speed v during one period will cover the distance equal to its length.

The wave period is the time when any wave point will make one full vibration.

The frequency (f) of the wave is the quantity informing us about the rate of repetition of the vibrations of a given point of the medium in which the wave propagates. Because the period is the duration of one full cycle of vibrations, the frequency (informing us about the number of cycles per unit of time) must be equal to its inverse:

By inserting the last expression into the wavelength formula we get:

Exercises

Glossary

Keywords

frequency of vibrationsfrequency of vibrationsfrequency of vibrations

harmonic oscillationsharmonic oscillationsharmonic oscillations

harmonic waveharmonic waveharmonic wave

vibration periodvibration periodvibration period

wave propagationwave propagationwave propagation