How is resonance related to standing waves

This experiment shows how AC oscillations from the generator become sound oscillations at the loudspeaker. Clamp the loudspeaker so that it faces upwards. Connect the low impedance output of the signal generator to the loudspeaker. Place a few grains of semolina or rice in the cone so that resonances show up clearly, as the generator frequency changes. The standing waves should be viewed stroboscopically, as well as by eye, to give students a clear understanding of their nature.

A microwave detector shows the standing wave pattern in the space between a microwave generator and a reflective metal barrier. Older equipment using a klystron tube uses hazardous voltages. The connectors on the leads between the transmitter and the power supply MUST be shielded types to minimize the risk of serious electric shock. The ventilation holes in the power supply may also give access to hazardous voltages, so its use MUST be closely supervised.

The transmitter should produce microwaves of about 3 cm. The microwaves can be unmodulated, in which case the receiver is connected to a meter. If they are modulated, it is possible to detect them using an amplifier and loudspeaker. A narrow probe receiver will better discriminate between nodes and antinodes than a horn receiver will.

Manufacturers usually supply a full instruction book, including experiments, with their microwave kits. Students find microwaves intriguing because of their invisibility. You may want to discuss how this is similar to other phenomena with which students are familiar; e.

This experiment, using what is often referred to as Kundt's tube, demonstrates vividly how sound waves make air vibrate in a tube. Place a thin layer of polystyrene beads along the length of the tube. Alternatively, you could use lycopodium powder or cork dust. These materials are best inserted by first sprinkling them along a metre rule, placing the rule inside the tube and then tipping them off.

Tape the loudspeaker in place. If the loudspeaker and tube have different diameters, join them with a paper cone or plastic cup. Put the vibrator on its side, attach one end of the spring to the vibrating element using string or a wire loop. Use the low impedance output of the signal generator, at full amplitude. With this experiment you can show standing waves, either transverse or longitudinal, in a rod or rods.

Three different experiments show standing waves having more than a single wavelength. To explain why each system behaves as it does, students need to understand both the factors affecting wave speed in a medium and also the relationship between wave speed and wavelength, for a given frequency. Rubber cords of different thickness: Tie the thick rubber cord to the thin elastic, and fix one of them to the vibrator. Since the wave velocity depends on the square root of the mass per unit length, an effective demonstration requires cords having a mass ratio of at least four.

Good lighting is important. Hanging chain: Chain sold for securing bath plugs is suitable. It is easiest to swing the top round in a small circle to generate a wave, but it will be clearer that a standing wave is involved if the top is oscillated sideways.

Rubber strip of varying width: Rubber cot sheet is a suitable material. Cut the sheet with a razor blade along previously marked lines, while it is being held down and lightly stretched. A piece 0. A line drawn down the middle helps to make the motion clear, especially as the edges of the strip tend to flap.

Stroboscopic illumination along the length of the strip is very effective. Use as large an amplitude of oscillation as can be managed. Teaching Guidance for Physics, more than any other science, can be demonstrated principle after principle by direct and simple experiments.

In some cases, it is clear that an experiment should be done either as a demonstration or as a class experiment. But many experiments can be done in either way, each having advantages and disadvantages.

Demonstration experiments can clarify a physical principle or show some interesting application of a principle. Make sure that students in the back row, as well as the front row, can see and hear what is going on. The best demonstration experiments avoid unnecessary detail — students can see and understand the whole working arrangement.

Other reasons for demonstrating experiments include safety reasons, and limited apparatus. Demonstrations can also be used as a part of a revision session or when you want to draw quick comparisons, e. In a short lesson, there may simply not be time for students to carry out their own investigations, after they have set up and dismantled ripple tanks.

Class experiments give students direct experience of physical phenomena. Just as important, they allow students to practise being scientists: discussing, developing hypotheses, designing experiments, predicting outcomes and returning to fresh hypotheses and more experiments.

They develop their powers of observation, thinking and problem-solving. Because some students work more quickly than others do, it is a good idea to give students a series of questions to pursue. With a selection of extra equipment set out cafeteria style, students can then proceed at their own pace. That way all remain engaged and faster students accomplish more. A wide range of mechanical and electromagnetic waves become understandable with a limited number of concepts, e. Practical experience of waves builds familiarity with wave phenomena on which future experience can be based.

Wave phenomena provide many interesting demonstrations and experiments which students can enjoy doing themselves. Many demonstrations require the development of skills for the effect to be clearly seen, and the acquisition of these skills is a pleasure in itself. In one of his autobiographical essays, Richard Feynman recounts his experience of finding that degree-level students were unable to connect optics theory with optical effects seen outside the classroom window.

Students have many opportunities to observe waves and ripples for themselves. This photo shows diffraction of ripples as they pass an obstruction in a pond. There are many excellent applets available online that show wave behaviour as if observing a ripple tank or oscilloscope screen.

These cannot substitute for experience of the phenomena themselves but provide a powerful way of helping students to visualize. They provide a valuable complement to experiments by removing extraneous effects.

Anything mechanical that can vibrate and has edges may have a standing wave on it. So the shaft driving a ship's propellers, or turning a turbine, can go into a standing wave oscillation, flexing as it turns. The wings of an aircraft also flex like a springy ruler. Two-dimensional standing waves are likely wherever flat panels can vibrate, so they matter to the motor and to the building engineer.

Three-dimensional standing waves are a problem for acoustic engineers. A good example is a loudspeaker cabinet enclosing a volume of vibrating air. Electromagnetic waves too can produce standing waves. Radio waves can form standing waves inside metal cavities. Radio waves have been used both to make very accurate measurements of the velocity of the waves, and in the design of powerful high frequency generators of microwaves.

Standing waves are an example of superposition. They occur when identical waves travelling in opposite directions. In the diagram below, P and Q represent points along a rope. At the instant shown, two wave trains travelling in opposite directions are just about to overlap at point P.

Points L1 to L4, R1 to R4 represent peaks or troughs along the wave train. Superposition at point P causes P to oscillate with amplitude 2A, since peaks L1 and R1 arrive there simultaneously, followed half a cycle later by troughs L2 and R2, etc. Careful inspection shows that superposition at Q will result in Q remaining stationary in space all the time.

The edges of any solid object act as boundaries to waves. Superposition of waves travelling towards the boundary with those reflected from it can lead to standing waves, if the object is vibrated at an appropriate frequency unless the vibrations are damped. Will the same equations work if there were symmetric boundary conditions with antinodes at each end?

What would the normal modes look like for a medium that was free to oscillate on each end? The free boundary conditions shown in the last Check Your Understanding may seem hard to visualize.

How can there be a system that is free to oscillate on each end? In part a , the rod is supported at the ends, and there are fixed boundary conditions at both ends. Given the proper frequency, the rod can be driven into resonance with a wavelength equal to length of the rod, with nodes at each end. In part b , the rod is supported at positions one quarter of the length from each end of the rod, and there are free boundary conditions at both ends.

Given the proper frequency, this rod can also be driven into resonance with a wavelength equal to the length of the rod, but there are antinodes at each end. Note that the study of standing waves can become quite complex.

In Figure The answer is no. In this configuration, there are additional conditions set beyond the boundary conditions. Since the rod is mounted at a point one quarter of the length from each side, a node must exist there, and this limits the possible modes of standing waves that can be created. We leave it as an exercise for the reader to consider if other modes of standing waves are possible. It should be noted that when a system is driven at a frequency that does not cause the system to resonate, vibrations may still occur, but the amplitude of the vibrations will be much smaller than the amplitude at resonance.

A field of mechanical engineering uses the sound produced by the vibrating parts of complex mechanical systems to troubleshoot problems with the systems. This may cause the engine to fail prematurely. The engineers use microphones to record the sound produced by the engine, then use a technique called Fourier analysis to find frequencies of sound produced with large amplitudes and then look at the parts list of the automobile to find a part that would resonate at that frequency.

The solution may be as simple as changing the composition of the material used or changing the length of the part in question. There are other numerous examples of resonance in standing waves in the physical world. The air in a tube, such as found in a musical instrument like a flute, can be forced into resonance and produce a pleasant sound, as we discuss in Sound. At other times, resonance can cause serious problems. A closer look at earthquakes provides evidence for conditions appropriate for resonance, standing waves, and constructive and destructive interference.

A building may vibrate for several seconds with a driving frequency matching that of the natural frequency of vibration of the building—producing a resonance resulting in one building collapsing while neighboring buildings do not.

Often, buildings of a certain height are devastated while other taller buildings remain intact. The building height matches the condition for setting up a standing wave for that particular height.

The span of the roof is also important. Often it is seen that gymnasiums, supermarkets, and churches suffer damage when individual homes suffer far less damage.

The roofs with large surface areas supported only at the edges resonate at the frequencies of the earthquakes, causing them to collapse. As the earthquake waves travel along the surface of Earth and reflect off denser rocks, constructive interference occurs at certain points. Often areas closer to the epicenter are not damaged, while areas farther away are damaged. Samuel J. Learning Objectives Describe standing waves and explain how they are produced Describe the modes of a standing wave on a string Provide examples of standing waves beyond the waves on a string.

Standing Waves Sometimes waves do not seem to move; rather, they just vibrate in place. The vibrations from the fan causes the surface of the milk to oscillate. The waves are visible due to the reflection of light from a lamp. The resulting wave is shown in black. These points are known as fixed points nodes. In between each two nodes is an antinode, a place where the medium oscillates with an amplitude equal to the sum of the amplitudes of the individual waves.

Nodes appear at integer multiples of half wavelengths. The nodes are marked with red dots and the antinodes are marked with blue dots. The string has a node on each end and a constant linear density.

The length between the fixed boundary conditions is L. The hanging mass provides the tension in the string, and the speed of the waves on the string is proportional to the square root of the tension divided by the linear mass density. A node occurs at each end of the string. The nodes are boundary conditions that limit the possible frequencies that excite standing waves.

Note that the amplitudes of the oscillations have been kept constant for visualization. The standing wave patterns possible on the string are known as the normal modes. Conducting this experiment in the lab would result in a decrease in amplitude as the frequency increases. The tension is provided by the weight of the hanging mass. The standing waves will depend on the boundary conditions. There must be a node at each end.

The first mode will be one half of a wave. The second can be found by adding a half wavelength. That is the shortest length that will result in a node at the boundaries. For example, adding one quarter of a wavelength will result in an antinode at the boundary and is not a mode which would satisfy the boundary conditions.

Since the wave speed velocity is the wavelength times the frequency, the frequency is wave speed divided by the wavelength. There is a node on one end, but an antinode on the other. Solution Begin with the velocity of a wave on a string. The tension is equal to the weight of the hanging mass.