Quiz
Q1) The distance between adjacent peaks in the direction of travel for a transverse wave is its
A. frequency.
B. period.
C. wavelength.
D. amplitude.
Answer) C.
The wavelength of a transverse wave is also the distance between adjacent troughs, or between any adjacent identical parts of the waveform.
Q2) The vibrations along a transverse wave move in a direction
A. along the wave.
B. perpendicular to the wave.
C. Both A and B.
D. Neither A nor B.
Answer) B.
The vibrations in a longitudinal wave, in contrast, are along (or parallel to) the direction of wave travel.
Transverse Wave Simulation
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(https://helpx.adobe.com/flash-player/kb/enabling-flash-player-chrome.html)
Mechanical Waves
You have learned how Newton’s laws of motion and conservation of energy principles govern the behavior of particles. These laws also govern the motion of waves. There are many kinds of waves. All kinds of waves transmit energy, including the waves you cannot see, such as the sound waves you create when you speak and the light waves that reflect from the leaves on the trees.
Transverse waves
A wave is a rhythmic disturbance that carries energy through matter or space. Water waves, sound waves, and the waves that travel down a rope or spring are types of mechanical waves.
A wave is a rhythmic disturbance that carries energy through matter or space. Water waves, sound waves, and the waves that travel down a rope or spring are types of mechanical waves.
Mechanical waves require a medium. Water, air, ropes, or springs are the materials that carry the energy of mechanical waves. Other kinds of waves, including electromagnetic waves and matter waves, will be described in later chapters. Because many of these waves cannot be directly observed, mechanical waves can serve as models for their study.
FIGURE 14–1 A quick shake of a rope sends out wave pulses in both directions.
The two disturbances that go down the rope shown in Figure 14–1 are called wave pulses. A wave pulse is a single bump or disturbance that travels through a medium. If the person continues to move the rope up and down, a continuous wave is generated. Notice that the rope is disturbed in the vertical direction, but the pulse travels horizontally.
This wave motion is called a transverse wave. A transverse wave is a wave that vibrates perpendicular to the direction of wave motion.
Speed and amplitude
How fast does a wave move? The speed of the pulse shown in Figure 14–4 can be found in the same way in which you would determine the speed of a moving car. First, you measure the displacement of the wave peak, $\Delta d$; then you divide this by the time interval, $\Delta t$, to find the speed, as shown by $\Delta v = \Delta d/ \Delta t$. The speed of a continuous wave, can be found the same way. For most mechanical waves, both transverse and longitudinal, the speed depends only on the medium through which the waves move.
How does the pulse generated by gently shaking a rope differ from the pulse produced by a violent shake? The difference is similar to the difference between a ripple in a pond and a tidal wave. They have different amplitudes. The amplitude of a wave is its maximum displacement from its position of rest, or equilibrium. Two similar waves having different amplitudes are shown in Figure 14–5.
FIGURE 14–5 The amplitude of wave A is larger than that of wave B.
A wave’s amplitude depends on how the wave is generated, but not on its speed. More work has to be done to generate a wave with a larger amplitude. For example, strong winds produce larger water waves than those formed by gentle breezes.
FIGURE 14–6 One end of a string, with a piece of tape at point P, is attached to a vibrating blade. Note the change in position of point P over time.
Waves with larger amplitudes transfer more energy. Thus, although a small wave might move sand on a beach a few centimeters, a giant wave can uproot and move a tree. For waves that move at the same speed, the rate at which energy is transferred is proportional to the square of the amplitude. Thus, doubling the amplitude of a wave increases the amount of energy it transfers each second by a factor of four.
Wavelength
Rather than focusing on one point on a wave, imagine taking a snapshot of a wave, so that you can see the whole wave at one instant in time. Figure 14–5 shows the low points, or troughs, and the high points, or crests, of a wave. The shortest distance between points where the wave pattern repeats itself is called the wavelength. Crests are spaced by one wavelength. Each trough is also one wavelength from the next. The Greek letter lambda, $\lambda $ , represents wavelength.
Period and frequency
Although wave speed and amplitude can describe both pulses and continuous waves, period ($\ T$) and frequency ($\ f$) apply only to continuous waves. You learned in Chapter 6 that the period of a simple harmonic oscillator, such as a pendulum, is the time it takes for the motion of the oscillator to repeat itself. Such an oscillator is usually the source, or cause, of a continuous wave. The period of a wave is equal to the period of the source. In Figure 14–6, the period, $\ T$, equals 0.04 s, which is the time it takes the source to return to the same point in its oscillation. The same time is taken by point P, a point on the rope, to return to its initial position.
The frequency of a wave, $\ f$, is the number of complete oscillations it makes each second. Frequency is measured in hertz. One hertz (Hz) is one oscillation per second. The frequency ($\ f$) and period ($\ T$) of a wave are related by the following equation.
Frequency of a Wave $\ f = \frac{1}{T}$
Both the period and the frequency of a wave depend only on its source. They do not depend on the wave’s speed or the medium. Although you can measure a wavelength directly, the wavelength depends on both the frequency of the oscillator and the speed of the wave. In the time interval of one period, a wave moves one wavelength.
Therefore, the speed of a wave is the wavelength divided by the period, $\lambda /T$. Because the frequency is more easily found than the period, this equation is more often written as
Speed of a Wave $\ v = \lambda f$.
How fast does a wave move? The speed of the pulse shown in Figure 14–4 can be found in the same way in which you would determine the speed of a moving car. First, you measure the displacement of the wave peak, $\Delta d$; then you divide this by the time interval, $\Delta t$, to find the speed, as shown by $\Delta v = \Delta d/ \Delta t$. The speed of a continuous wave, can be found the same way. For most mechanical waves, both transverse and longitudinal, the speed depends only on the medium through which the waves move.
How does the pulse generated by gently shaking a rope differ from the pulse produced by a violent shake? The difference is similar to the difference between a ripple in a pond and a tidal wave. They have different amplitudes. The amplitude of a wave is its maximum displacement from its position of rest, or equilibrium. Two similar waves having different amplitudes are shown in Figure 14–5.
A wave’s amplitude depends on how the wave is generated, but not on its speed. More work has to be done to generate a wave with a larger amplitude. For example, strong winds produce larger water waves than those formed by gentle breezes.
Waves with larger amplitudes transfer more energy. Thus, although a small wave might move sand on a beach a few centimeters, a giant wave can uproot and move a tree. For waves that move at the same speed, the rate at which energy is transferred is proportional to the square of the amplitude. Thus, doubling the amplitude of a wave increases the amount of energy it transfers each second by a factor of four.
Wavelength
Rather than focusing on one point on a wave, imagine taking a snapshot of a wave, so that you can see the whole wave at one instant in time. Figure 14–5 shows the low points, or troughs, and the high points, or crests, of a wave. The shortest distance between points where the wave pattern repeats itself is called the wavelength. Crests are spaced by one wavelength. Each trough is also one wavelength from the next. The Greek letter lambda, $\lambda $ , represents wavelength.
Period and frequency
Although wave speed and amplitude can describe both pulses and continuous waves, period ($\ T$) and frequency ($\ f$) apply only to continuous waves. You learned in Chapter 6 that the period of a simple harmonic oscillator, such as a pendulum, is the time it takes for the motion of the oscillator to repeat itself. Such an oscillator is usually the source, or cause, of a continuous wave. The period of a wave is equal to the period of the source. In Figure 14–6, the period, $\ T$, equals 0.04 s, which is the time it takes the source to return to the same point in its oscillation. The same time is taken by point P, a point on the rope, to return to its initial position.
The frequency of a wave, $\ f$, is the number of complete oscillations it makes each second. Frequency is measured in hertz. One hertz (Hz) is one oscillation per second. The frequency ($\ f$) and period ($\ T$) of a wave are related by the following equation.
Frequency of a Wave $\ f = \frac{1}{T}$
Both the period and the frequency of a wave depend only on its source. They do not depend on the wave’s speed or the medium. Although you can measure a wavelength directly, the wavelength depends on both the frequency of the oscillator and the speed of the wave. In the time interval of one period, a wave moves one wavelength.
Therefore, the speed of a wave is the wavelength divided by the period, $\lambda /T$. Because the frequency is more easily found than the period, this equation is more often written as
Speed of a Wave $\ v = \lambda f$.