¿Cuánto sabes sobre ondas y vibraciones?

Introduction to Waves and Vibrations

• The course is about waves and vibrations, and how they relate to oscillations, periodic, and not so periodic events in the world.

• Many actions in daily life are periodic, such as heartbeat, breathing, and daily routines.

• Even liquids can exhibit periodic motion, such as the glop, glop, glop of liquid pouring or the movement of a toy that transfers liquid in 17 seconds.

• Objects like plates, toys, and balls can exhibit both musilly and wobbling motion, and the frequency of these motions can change over time.

• Even wind can generate periodic motion, such as the waving of hair or a flag.

• Simple harmonic oscillations are extremely common in nature and can be written as x = x0cos(ωt+φ).

• The amplitude (x0), angular frequency (ω), and phase angle (φ) are important parameters in simple harmonic motion.

• An example of simple harmonic motion is a spring system, where the frequency is independent of the initial conditions and is determined by the spring constant (K) and mass (M).

• The same spring system can also oscillate vertically due to gravity, and the frequency remains the same.

• Sound is also a form of wave propagation, where pressure waves are generated by oscillating vocal chords and travel through the air to reach the eardrum.

• The frequency of sound can be tested using a tuning fork, and most humans can hear frequencies between 20 Hz and 20 kHz.

• Loss of hearing in higher frequencies is a common occurrence with age.Uniform Circular Motion and Complex Numbers

• Uniform circular motion can be projected as shadow projection and can be made to appear as simple harmonic motion by matching the period of oscillation of a spring with the time it takes for the object to go around.

• The period for a spring system is 2 pi times the square root of M over K.

• Measurement without uncertainty in physics is meaningless.

• Accurate measurement for the period can be obtained by making 10 oscillations because the error in T goes down by a factor of ten.

• The mass of the spring can affect the period of oscillation and must be taken into account.

• The period of oscillation is a good approximation when the mass of the spring itself is capital M, and if capital M divided by 3 is substantially less than the mass at the end of the spring.

• Friction has a negligible effect on the measurement of the periods.

• Complex numbers can simplify problem-solving in physics.

• A complex number can be represented as a position on a complex plane with a real and imaginary axis.

• Euler's formula states that e to the power of Jtheta is equal to cosine theta plus J times sine theta.

• A simple harmonic motion can be represented as a real part of a complex number.

• The amplitude and phase angle can be included in the representation of a complex number.Walter Lewin's Lecture on Oscillations and Simple Harmonic Motion

• The lecture provides practice problems and cases for students to work on.

• The problem of J to the power J is introduced, which has an infinite number of solutions.

• J can also be expressed as E to the power J times pi over two.

• There will be a mini quiz during some of the five-minute breaks on Tuesdays.

• A demonstration of an oscillation produced by heat and cooling is shown.

• The period of oscillations for a pendulum is given by two pi times the square root of L over G.

• The period of oscillations is independent of the mass of the object in a pendulum.

• The mother of all pendulums in 26-100 is 5.18 m long and has a period predicted to be 4.57 plus or minus 0.02 seconds.

• A physical pendulum is more complex and has a center of mass and a point of origin.

• The torque relative to the point of origin is found to determine the period of oscillations.

• The lecture provides a detailed explanation of how to deal with physical pendulums.

• The lecture concludes with a demonstration of how to calculate the period of oscillations for a physical pendulum.Simple Harmonic Motion and the Period of Oscillation

• Torque is perpendicular to the blackboard and is calculated using the cross product of force and distance.

• The torque equation is -BMG(theta)/I(P) = theta''.

• Small angle approximation is applied to solve the differential equation for simple harmonic oscillation.

• theta = theta0cos(omegat+phi), where omega is the square root of BMG/I(P).

• The period of oscillation is I(P)/BMG.

• Angular frequency is a given and should not be confused with angular velocity.

• The moment of inertia about the point of rotation is calculated using the parallel axis theorem.

• The period of oscillation for a hoop is predicted to be 2pisqrt(2R/G).

• The radius of the hoop is measured as 40.0 +/- 0.5 cm.

• The prediction for the period of oscillation for the hoop is 1.795 +/- 0.01 seconds.

• The period of oscillation is observed to be 17.80 seconds, within the predicted range.

• The timer is started when the object comes to a halt, not when it goes through equilibrium.

Introduction to Waves and Vibrations

• The course is about waves and vibrations, and how they relate to oscillations, periodic, and not so periodic events in the world.

• Many actions in daily life are periodic, such as heartbeat, breathing, and daily routines.

• Even liquids can exhibit periodic motion, such as the glop, glop, glop of liquid pouring or the movement of a toy that transfers liquid in 17 seconds.

• Objects like plates, toys, and balls can exhibit both musilly and wobbling motion, and the frequency of these motions can change over time.

• Even wind can generate periodic motion, such as the waving of hair or a flag.

• Simple harmonic oscillations are extremely common in nature and can be written as x = x0cos(ωt+φ).

• The amplitude (x0), angular frequency (ω), and phase angle (φ) are important parameters in simple harmonic motion.

• An example of simple harmonic motion is a spring system, where the frequency is independent of the initial conditions and is determined by the spring constant (K) and mass (M).

• The same spring system can also oscillate vertically due to gravity, and the frequency remains the same.

• Sound is also a form of wave propagation, where pressure waves are generated by oscillating vocal chords and travel through the air to reach the eardrum.

• The frequency of sound can be tested using a tuning fork, and most humans can hear frequencies between 20 Hz and 20 kHz.

• Loss of hearing in higher frequencies is a common occurrence with age.Uniform Circular Motion and Complex Numbers

• Uniform circular motion can be projected as shadow projection and can be made to appear as simple harmonic motion by matching the period of oscillation of a spring with the time it takes for the object to go around.

• The period for a spring system is 2 pi times the square root of M over K.

• Measurement without uncertainty in physics is meaningless.

• Accurate measurement for the period can be obtained by making 10 oscillations because the error in T goes down by a factor of ten.

• The mass of the spring can affect the period of oscillation and must be taken into account.

• The period of oscillation is a good approximation when the mass of the spring itself is capital M, and if capital M divided by 3 is substantially less than the mass at the end of the spring.

• Friction has a negligible effect on the measurement of the periods.

• Complex numbers can simplify problem-solving in physics.

• A complex number can be represented as a position on a complex plane with a real and imaginary axis.

• Euler's formula states that e to the power of Jtheta is equal to cosine theta plus J times sine theta.

• A simple harmonic motion can be represented as a real part of a complex number.

• The amplitude and phase angle can be included in the representation of a complex number.Walter Lewin's Lecture on Oscillations and Simple Harmonic Motion

• The lecture provides practice problems and cases for students to work on.

• The problem of J to the power J is introduced, which has an infinite number of solutions.

• J can also be expressed as E to the power J times pi over two.

• There will be a mini quiz during some of the five-minute breaks on Tuesdays.

• A demonstration of an oscillation produced by heat and cooling is shown.

• The period of oscillations for a pendulum is given by two pi times the square root of L over G.

• The period of oscillations is independent of the mass of the object in a pendulum.

• The mother of all pendulums in 26-100 is 5.18 m long and has a period predicted to be 4.57 plus or minus 0.02 seconds.

• A physical pendulum is more complex and has a center of mass and a point of origin.

• The torque relative to the point of origin is found to determine the period of oscillations.

• The lecture provides a detailed explanation of how to deal with physical pendulums.

• The lecture concludes with a demonstration of how to calculate the period of oscillations for a physical pendulum.Simple Harmonic Motion and the Period of Oscillation

• Torque is perpendicular to the blackboard and is calculated using the cross product of force and distance.

• The torque equation is -BMG(theta)/I(P) = theta''.

• Small angle approximation is applied to solve the differential equation for simple harmonic oscillation.

• theta = theta0cos(omegat+phi), where omega is the square root of BMG/I(P).

• The period of oscillation is I(P)/BMG.

• Angular frequency is a given and should not be confused with angular velocity.

• The moment of inertia about the point of rotation is calculated using the parallel axis theorem.

• The period of oscillation for a hoop is predicted to be 2pisqrt(2R/G).

• The radius of the hoop is measured as 40.0 +/- 0.5 cm.

• The prediction for the period of oscillation for the hoop is 1.795 +/- 0.01 seconds.

• The period of oscillation is observed to be 17.80 seconds, within the predicted range.

• The timer is started when the object comes to a halt, not when it goes through equilibrium.

Normal modes in continuous media: el ejemplo de la cuerda fija en ambos extremos.

1. El profesor Frank Wilczek de MIT acaba de recibir el Premio Nobel de Física por su trabajo en cromodinámica cuántica.

2. Se aborda el estudio de los modos normales en medios continuos, comenzando con una cuerda fija en ambos extremos.

3. La forma de la cuerda se puede describir mediante una ecuación senoidal en función de la amplitud, la longitud de onda y la velocidad de propagación.

4. La velocidad de propagación depende de la tensión y la masa por unidad de longitud de la cuerda.

5. La ecuación senoidal es una solución a la ecuación de onda.

6. La longitud de onda se define como la distancia que recorre la perturbación en un tiempo de una oscilación.

7. Se introduce una nueva variable, el número de onda K, que se define como 2π dividido por la longitud de onda.

8. Se puede reescribir la ecuación senoidal en términos de K y la frecuencia angular, lo que facilita el cálculo de la frecuencia.

9. Al generar dos ondas en direcciones opuestas, se puede obtener una onda estacionaria, también conocida como una onda de pie.

10. La cuerda fija en ambos extremos solo permitirá ciertos valores de K, que están determinados por las condiciones de contorno.

11. Estos valores de K permiten la existencia de frecuencias de resonancia discretas, que se conocen como modos normales o frecuencias naturales.

12. La cuerda puede vibrar simultáneamente en múltiples modos normales, cada uno de los cuales tiene su propia amplitud y frecuencia.Demostración de modos normales y medición de la velocidad del sonido

13. La demostración se enfoca en los modos normales, que resultan en ondas estacionarias.

14. Se utiliza una manguera de goma para generar una onda estacionaria en el quinto armónico.

15. La frecuencia de resonancia cambia cuando se mueve la mesa debido a la velocidad del sonido.

16. Se utiliza una luz estroboscópica para hacer que la cuerda parezca estar quieta y se pueden ver los nodos y antinodos.

17. Se pueden aplicar los mismos principios a las ondas de sonido en un tubo cerrado.

18. La velocidad del sonido es una constante de 300 m/s.

19. La longitud del tubo es la única variable que se puede cambiar en los instrumentos de viento.

20. Se puede medir la velocidad del sonido midiendo la longitud de onda y la frecuencia.

21. Se utiliza un micrófono y un altavoz para demostrar los nodos y antinodos en el tubo.

22. Se utiliza una regla para medir la distancia entre los nodos y se calcula la velocidad del sonido.

23. La velocidad del sonido se mide con una precisión de +/- 2 m/s.

24. La demostración muestra cómo los modos normales se aplican tanto a las ondas de sonido como a las ondas de cuerda.Energía en ondas viajeras y de pie

25. Una onda viajera tiene energía debido al movimiento en la dirección Y, no por la masa que se mueve a lo largo de la onda.

26. La energía cinética en una sección pequeña de una onda viajera es 1/2 veces la masa por unidad de longitud (mu) multiplicada por la velocidad en la dirección Y al cuadrado.

27. La energía cinética total en una longitud de onda es la integral de la energía cinética en una sección pequeña de la onda viajera.

28. La energía cinética total en una longitud de onda es proporcional al cuadrado de la amplitud (A) de la onda viajera.

29. La energía potencial en una longitud de onda es igual a la energía cinética en una longitud de onda.

30. La energía total en una onda viajera es igual a la suma de la energía cinética y la energía potencial.

31. En una onda de pie, la energía total es igual a la energía potencial debido a que no hay movimiento en la dirección Y.

32. La energía en dos ondas viajeras con amplitud 1/2A es igual a la energía en una onda de pie con amplitud A.

33. La potencia necesaria para generar una onda viajera es proporcional a la longitud de onda y la velocidad de propagación.

34. La energía y la potencia se pueden transferir de una onda a otra sin que la masa se mueva.

35. Las condiciones de frontera de una onda en un punto de unión deben ser iguales en ambos lados de la frontera.

36. Para calcular la onda reflejada y la onda transmitida en un punto de unión, se deben usar las condiciones de frontera y las leyes de Snell.Reflexión y transmisión de ondas en cuerdas

37. El texto trata sobre la reflexión y transmisión de ondas en cuerdas.

38. Las cuerdas deben tener una continuidad en su tensión y dirección para evitar kinks.

39. La continuidad se logra al tener una derivada espacial igual en ambos lados de la unión.

40. Se parte de una onda incidente con amplitud A de I y frecuencia omega.

41. La onda reflejada tiene la misma frecuencia pero amplitud A de R.

42. La onda transmitida también tiene la misma frecuencia pero amplitud A transmitida.

43. Las ecuaciones son dos con tres incógnitas: AI, AR y A transmitida.

44. Se busca el ratio de las amplitudes de lo que entra y lo que sale.

45. Se pueden calcular los ratios de las amplitudes con las ecuaciones.

46. Si mu2 es infinitamente grande, es un extremo fijo y R es -1 y TR es 0.

47. Si mu1 es mayor que mu2, entonces R es mayor que 0 y TR también es mayor que 0.

48. Si mu1 es igual a mu2, entonces R es 0 y TR es 1.