Wave Speed. Presentation Outline Review – Frequency illustrated – Frequency and period relationship calculations – Wavelength, Amplitude, Crest, Trough.

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Presentation transcript:

Wave Speed

Presentation Outline Review – Frequency illustrated – Frequency and period relationship calculations – Wavelength, Amplitude, Crest, Trough – Transverse vs. Longitudinal Animation Wave Speed - independent of frequency Standing Wave Demonstration and Derivation of Wave Equation Wave Equation and Examples Wave Practice

Frequency The number of vibrations an object makes in a unit of time is an object’s frequency. The frequency specifies the number of back-and-forth vibrations in one second.

The unit of frequency is called the hertz (Hz). A frequency of one “cycle per second” is 1 hertz, two cycles per second is 2 hertz, and so on. Higher frequencies are measured in kilohertz (kHz—thousands of hertz) = 10 3 Hz megahertz (MHz—millions of hertz) = 10 6 Hz gigahertz (GHz—billions of hertz) = 10 9 Hz Frequency Units

If the frequency of a vibrating object is known, its period can be calculated, and vice versa. Suppose, for example, that a pendulum makes two vibrations in one second. Its frequency is ____ Hz. The time needed to complete one vibration—that is, the period of vibration—is 1/2 second. As you can see below, frequency and period are inverses of each other: Frequency and Period

If the frequency of a vibrating object is known, its period can be calculated, and vice versa. Suppose, for example, that a pendulum makes two vibrations in one second. Its frequency is ____ Hz. The time needed to complete one vibration—that is, the period of vibration—is 1/2 second. As you can see below, frequency and period are inverses of each other: Frequency and Period

think! What is the frequency in vibrations per second of a 100-Hz wave? 25.2 Wave Description

think! What is the frequency in vibrations per second of a 100-Hz wave? Answer: A 100-Hz wave vibrates 100 times/s Wave Description

think! The Sears Tower in Chicago sways back and forth at a frequency of about 0.1 Hz. What is its period of vibration? 25.3 Wave Motion

think! The Sears Tower in Chicago sways back and forth at a frequency of about 0.1 Hz. What is its period of vibration? Answer: The period is 25.3 Wave Motion

Two Types of Waves Transverse Wave Transverse waves carry energy when the parts of the wave move away from equilibrium in a direction perpendicular to the motion of the wave. An example of a transverse wave is an electromagnetic wave (light). Longitudinal Wave Longitudinal waves carry energy when the parts of the wave move away from equilibrium in a direction parallel to the motion of the wave. An example of a longitudinal wave is a sound wave.

WAVE SPEED

The speed of a wave describes how quickly the wave disturbance moves across a medium. The speed of a wave depends only on the medium through which the wave moves, not on the frequency of the wave. If the wavelength is 1 meter, and one wavelength per second passes the pole, then the speed of the wave is 1 m/s. Wave Speed

The speed of a wave describes how quickly the wave disturbance moves across a medium. The speed of a wave depends only on the medium through which the wave moves. Speed is equal to the distance travelled divided by the time it takes to travel the distance. As an example, let’s say the distance traveled is the wavelength of a wave. By definition, the time to complete one wavelength is known as the period, so the equation becomes: Wave Speed

The speed of a wave describes how quickly the wave disturbance moves across a medium. The speed of a wave depends only on the medium through which the wave moves. Speed is equal to the distance travelled divided by the time it takes to travel the distance. As an example, let’s say the distance traveled is the wavelength of a wave. By definition, the time to complete one wavelength is known as the period, so the equation becomes: Wave Speed

The speed of a wave describes how quickly the wave disturbance moves across a medium. The speed of a wave depends only on the medium through which the wave moves. Speed is equal to the distance travelled divided by the time it takes to travel the distance. As an example, let’s say the distance traveled is the wavelength of a wave. By definition, the time to complete one wavelength is known as the period, so the equation becomes: Wave Speed

WALKING DEMONSTRATION Walk with 1-meter steps with a frequency of 1 Hz. Waves travel the same speed for the same medium… Walk with 0.5 meter steps, what will the frequency become? Walk with 0.25 meter steps, what will the frequency become?

SPEAKERS AND ELASTIC STRINGS

Frequency (Hz)Wavelength (m)Wave Speed (m/s)

Wavelength and frequency vary inversely to produce the same wave speed for all sounds. Wave Speed

WAVE EQUATION EXAMPLES

think! If a water wave vibrates up and down two times each second and the distance between wave crests is 1.5 m, what is the frequency of the wave? What is its wavelength? What is its speed? 25.4 Wave Speed

think! If a water wave vibrates up and down two times each second and the distance between wave crests is 1.5 m, what is the frequency of the wave? What is its wavelength? What is its speed? Answer: The frequency of the wave is 2 Hz; its wavelength is 1.5 m; and its wave speed is 25.4 Wave Speed

think! The speed of sound is about 343 m/s. What is the wavelength of a 680-Hz sound wave? 25.4 Wave Speed

WAVE PRACTICE