How long is an oscillation

As the wave moves by, in a time equal to the period one oscillation of the wave occurs and so the wave has moved along a distance equal to the wavelength. The velocity of the wave is then given by. In the case of water waves, for example, the distance from the one peak to the next or one valley to the next is one wavelength see the figure just above. Notice that this measure, wavelength, then depends not only on the speed of propagation of the wave, but also on the period or frequency of the vibration.

Not only do waves behave very differently from material objects in the context of transmission of momentum and energy, but they also interact with each other differently than material objects do. When two objects meet each other they collide. Two waves, on the other hand, do not interact at all but pass "through" each other as ghosts pass through ghosts.

But in the region where the two passing waves overlap the effective disturbance becomes a net sum of the disturbances of the two waves. So, when a floater happens to be "at the wrong place at the wrong time", i.

But were it lucky to be where the peak of one wave meets the valley of another wave of equal amplitude, then it would not move at all; as if there were no waves passing by. This addition of disturbance, which does not affect the original waves, is purely a wave phenomenon and is called interference. So, waves do not collide, they interfere. Exercise: to see how two waves interfere, work with the applet: Wave Interference Try changing the wavelength of the waves and their amplitudes.

One of the interesting results is when the two waves have the same amplitudes and almost the same wavelengths, but not quite. Another wave characteristic that has no analog when it comes to travel of material objects is that when a wave reaches an obstacle or an opening , with dimensions comparable to its wavelength, it bends around the obstacle and about the opening. This second wave phenomena is called the diffraction effect. Check the applet on Wave Diffraction to see how this works.

Try changing the opening size to see how the effects of diffraction sharpen up or get washed out. Questions on Waves. Electrically charged objects attract or repel each other, just as two magnets attract or repel each other.

The electric force that acts between charges has significant differences from the magnetic force that results in the interaction of magnets. But, for the topic at hand, these forces behave very much the same way in that they are both of the " action-at-a-distance " type.

That is to say, these forces manifest themselves in the absence of any physical contact between the objects that interact with each other. For example, two magnets exert forces on each other even while they are apart and neither is touching the other. In fact, the reason that a compass works is that its small magnetized needle rotates because of the magnetic force of the earth, as if manipulated by a ghost. Another way model of explaining this interaction is to state that the earth's magnetic core establishes a magnetic field everywhere in space.

It is this field that affects the compass needle. This concept of "field" is useful because once we know the field of the earth, then we know how any magnet would be affected once it enters this field.

The field provides an intermediary to understand how action at a distance can work. With electric charges, each charge produces an electric field which then in turn interacts with other electric charges. Another advantage of the field concept is that it allows for an easier visualization of what happens when one of the charges or magnets begins to move.

In this view, when a charge changes position, the field that it produces also changes in space. In fact, as the charge oscillates, so does its field. This oscillating field is what is called an electromagnetic wave. By making a charge oscillate at one point in space we can cause another charge located further away to undergo oscillatory motion. Similar to mechanical waves, such as sound and water waves, electromagnetic waves are characterized by their frequency, speed, and amplitude.

The above picture shows how both the magnetic and electric fields oscillate as the wave propagates to the right. One interesting aspect of an electromagnetic wave that sets it apart from all other waves we have examined so far is that its propagation requires no medium. Water waves, which are transverse, of course need water to propagate in. Sound waves, which are longitudinal, also need a matter medium; although almost any type of matter would do for them sound travels in air, all known gases, in fluids, in solids, and in plasma, a gas of charged ions.

But oscillating electromagnetic fields travel even in vacuum. Another interesting feature of electromagnetic waves relates to their speed of propagation.

Mechanical waves travel with a speed that is characteristic of their medium of travel. For example, sound travels much faster in metals than it does in air. Its speed of travel in air is also dependant on the air pressure, temperature, and humidity.

In the same way, the speed of propagation of electromagnetic waves depends on the material it is passing through, even though it does not "need" the material for its propagation.

But what is most significant is that this speed, to our knowledge, is the fastest possible way that nature allows for transmission of energy and momentum.

As the sound wave is directed at the glass, the glass responds by resonating at the same frequency as the sound wave.

With enough energy introduced into the system, the glass begins to vibrate and eventually shatters. Do you think there is any harmonic motion in the physical world that is not damped harmonic motion? Try to make a list of five examples of undamped harmonic motion and damped harmonic motion.

Which list was easier to make? All harmonic motion is damped harmonic motion, but the damping may be negligible.

This is due to friction and drag forces. It is easy to come up with five examples of damped motion: 1 A mass oscillating on a hanging on a spring it eventually comes to rest. As for the undamped motion, even a mass on a spring in a vacuum will eventually come to rest due to internal forces in the spring. Damping may be negligible, but cannot be eliminated. How much energy must the shock absorbers of a kg car dissipate in order to damp a bounce that initially has a velocity of 0.

Assume the car returns to its original vertical position. Calculate the energy stored in the spring by this stretch, and compare it with the gravitational potential energy. Explain where the rest of the energy might go. Suppose you have a 0. There is simple friction between the object and surface with a static coefficient of friction. Suppose you attach an object with mass m to a vertical spring originally at rest, and let it bounce up and down.

The amplitude of the motion is the distance between the equilibrium position of the spring without the mass attached and the equilibrium position of the spring with the mass attached.

A diver on a diving board is undergoing SHM. Her mass is The next diver is a male whose period of simple harmonic oscillation is 1. What is his mass if the mass of the board is negligible? Suppose a diving board with no one on it bounces up and down in a SHM with a frequency of 4.

The board has an effective mass of What is the frequency of the SHM of a The device pictured in the following figure entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring. The equilibrium position is marked at zero. A student moves the mass out to. The mass oscillates in SHM. At what rate will a pendulum clock run on the Moon, where the acceleration due to gravity is. If a pendulum-driven clock gains 5. Write an equation for the motion of the hanging mass after the collision.

Assume air resistance is negligible. Write an equation for the motion of the system after the collision. It can be modeled as a physical pendulum as a rod oscillating around one end. By what percentage will the period change if the temperature increases by. A second block of 0. The 2. There is a coefficient of friction of 0. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building.

Parcels of air small volumes of air in a stable atmosphere where the temperature increases with height can oscillate up and down, due to the restoring force provided by the buoyancy of the air parcel. The frequency of the oscillations are a measure of the stability of the atmosphere.

Assuming that the acceleration of an air parcel can be modeled as. Note that in a stable atmosphere, the density decreases with height and parcel oscillates up and down. What time will the clock read Search for:. Period and Frequency in Oscillations Learning Objectives By the end of this section, you will be able to: Observe the vibrations of a guitar string. Determine the frequency of oscillations. Example 1. Determine the Frequency of Two Oscillations: Medical Ultrasound and the Period of Middle C We can use the formulas presented in this module to determine both the frequency based on known oscillations and the oscillation based on a known frequency.

A medical imaging device produces ultrasound by oscillating with a period of 0. What is the frequency of this oscillation?

The frequency of middle C on a typical musical instrument is Hz. What is the time for one complete oscillation? Strategy Both Parts 1 and 2 can be answered using the relationship between period and frequency.

Solution for Part 1 Substitute 0. Discussion for Part 1 The frequency of sound found in Part 1 is much higher than the highest frequency that humans can hear and, therefore, is called ultrasound. Check your Understanding Identify an event in your life such as receiving a paycheck that occurs regularly. Solution I visit my parents for dinner every other Sunday. If your heart rate is beats per minute during strenuous exercise, what is the time per beat in units of seconds?

Find the frequency of a tuning fork that takes 2. A stroboscope is set to flash every 8. What is the frequency of the flashes?