THE WAVE MOTION

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The Wave Model

The distance from one crest to the next is called the wavelength λ (Greek letter lambda). More generally, the wavelength is the minimum distance between any two identical points (such as the crests) on adjacent waves

If you count the number of seconds between the arrivals of two adjacent waves, you are measuring the period T of the waves. In general, the period is the time required for two identical points (such as the crests) of adjacent waves to pass by a point.

In general, the frequency of a periodic wave is the number of crests (or troughs, or any other point on the wave) that pass a given point in a unit time interval.

The maximum displacement of a particle of the medium is called the amplitude A of the wave.

Time Period, Frequency, Velocity and Wavelength

From the definitions above the relationships among features of a wave can be summarised as follows:

Wave Model

1. An off-shore swell consists of waves with a wavelength of 10 m. The frequency of those waves passing a fixed point was measured at 0.5 Hz. What is the velocity of the wave motion?

Wave Model

2. Light, an electromagnetic wave, travels at 3.00 × 108 m s−1. What is the frequency of green light of wavelength 550 nm (550 × 10−9 m)?

Wave Model

3. A tsunami wave is detected by an early warning buoy in the Pacific Ocean. It has a period of 50.0 s. Satellite tracking shows that the wavelength of the waves is 10.0 km. From this information, the speed of the tsunami in the ocean can be found. What is its speed?

Wave Model

3. A tsunami wave is detected by an early warning buoy in the Pacific Ocean. It has a period of 50.0 s. Satellite tracking shows that the wavelength of the waves is 10.0 km. From this information, the speed of the tsunami in the ocean can be found. What is its speed?

Wave Model

10. The graph shows a snapshot of a transverse travelling wave at time t = 0 s.

(a) The vertical distance between points A and B is equal to 1.3 m. The horizontal distance between points A and B is 2.0 m. Calculate the value of the amplitude and the wavelength of the wave shown above.(b) A snapshot is taken of the wave in the preceding question at a time t = 24 s. The snapshot shows the wave in exactly the same position as in the diagram above. Which one of the values below could be a measure of the period of the transverse wave?(i) 12 s (ii) 18 s (iii) 36 s (iv) 48 s(c) Use your answer to part (a) and (b) to calculate the speed of the wave.

Energy Transformation in Waves

In modern communication devices, a series of energy transformations is required in order to transfer information from one place to another. For example:Microphones transform sound energy into electrical signals.In speakers, electrical signals cause a small diaphragm to vibrate, in turn causing vibrations in the air particles, which then radiate out as sound energy. Hence electrical energy is transformed into mechanical energy and then mechanical energy is transformed into sound energy.In radio, television and mobile telephones, electrical signals are used to modulate radio waves so that information is sent from the aerial of the transmitting device to the aerial of the receiving device. However, mobile telephones do not connect with each other directly. Their signals go through the nearest base station and the telephone company’s wire and fibre optic networks to the base station that is closest to the other telephone.

Television (radio is similar):1. Light and Sound Energy → Electrical Energy2. Electrical Energy → Electromagnetic Radiation3. Electromagnetic Radiation → Electrical Energy [In mobile tower to exchange]4. Electrical Energy → Light and Sound Energy

Types of Waves

1. Mechanical Waves

(a) Transverse Waves: In a transverse wave, the particles of the medium vibrate in a plane that is perpendicular to the direction of propagation of the wave.

(b) Longitudinal Waves: A traveling wave that causes the particles of the medium to move parallel to the direction of wave motion is called a longitudinal wave.

2. Electromagnetic Waves

One, Two and Three Dimensional Waves

One, Two and Three Dimensional Waves

One Dimensional Wave: A one-dimensional wave is confined to that medium and can travel in one direction only. An example of a wave travelling in one dimension is the motion of either a transverse or longitudinal wave in a slinky, or a transverse wave travelling along a rope. In this case the medium confines the wave to the rope or slinky. The energy of the wave motion has only one dimension in which to travel. Two Dimensional Wave: A two dimensional wave spreads out, dispersing the energy over a larger area as it travels. An example of a wave travelling in two dimensions is a transverse wave travelling from a point source of disturbance in still water. A pebble thrown into a still, flat-bottomed pond will produce a wave travelling outwards with a circular wavefront away from the initial disturbance Three Dimensional Wave: As an example of waves travelling in three dimensions, consider a point source of sound - it results in a sound wave that immediately travels away from the source in three dimensions with a spherical wavefront. Similarly, a point source of light will illuminate a three-dimensional space.