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A surfer needs to understand the properties of waves.

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Frequency and Period

What determines the frequency of a wave?

Any periodic motion has a frequency, which is the number of complete cycles in a given time.

A wave’s frequency equals the frequency of the vibrating source producing the wave.

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Any motion that repeats at regular time intervals is called periodic motion.

    • The time required for one cycle is called the period.
    • Frequency is the number of complete cycles in a given time.
    • Frequency is measured in cycles per second, or hertz (Hz).

Frequency and Period

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  1. A wave vibrating at one cycle per second has a frequency of 1.0 Hz.
  2. A wave vibrating at two cycles per second has a frequency of 2.0 Hz.

Frequency and Period

Frequency = 1.0 hertz�One cycle per second

Frequency = 2.0 hertz�Two cycles per second

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Wavelength

How are frequency and wavelength related?

Wavelength is the distance between a point on one wave and the same point on the next cycle of the wave.

Increasing the frequency of a wave decreases its wavelength.

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For a transverse wave, wavelength is measured between adjacent crests or between adjacent troughs.

For a longitudinal wave, wavelength is the distance between adjacent compressions or rarefactions.

Wavelength

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Wavelength can be measured from any point on a wave to the same point on the next cycle of the wave.

Wavelength

Long wavelength

Short wavelength

Rest position

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Wave Speed

How are frequency, wavelength, and speed related?

If you assume that waves are traveling at a constant speed, then wavelength is inversely proportional to frequency.

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When the wavelength is in meters, and the frequency is in hertz, the units for speed are meters per second.

The speed of a wave is also calculated by dividing its wavelength by its period.

Wave Speed

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Speed of Mechanical Waves

One end of a rope is vibrated to produce a wave with a wavelength of 0.25 meter. The frequency of the wave is 3.0 hertz. What is the speed of the wave?

Wave Speed

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Read and Understand

What information are you given?

​

Wave Speed

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Read and Understand

What information are you given?

​

Wave Speed

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Plan and Solve

What unknown are you trying to calculate?

​

​

What formula contains the given quantities and the unknown?

Wave Speed

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Plan and Solve

What unknown are you trying to calculate?

​

​

What formula contains the given quantities and the unknown?

Wave Speed

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Plan and Solve

Replace each variable with its known value.

Wave Speed

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Plan and Solve

Replace each variable with its known value.

Wave Speed

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Look Back and Check

Is your answer reasonable?�

Wave Speed

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Look Back and Check

Is your answer reasonable?�

Because the frequency is 3.0 hertz, the wave should travel a distance of 3 wavelengths in 1 second. This distance is 0.75 meters, which agrees with the calculated speed of 0.75 m/s.

Wave Speed

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1. A wave on a rope has a wavelength of 2.0 m and a frequency of 2.0 Hz. What is the speed of the wave? ��Answer:

Wave Speed

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1. A wave on a rope has a wavelength of 2.0 m and a frequency of 2.0 Hz. What is the speed of the wave? ��Answer: ��The speed is 2.0 m × 2.0 Hz = 4.0 m/s

Wave Speed

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2. A motorboat is tied to a dock with its motor running. The spinning propeller makes a surface wave in the water with a frequency of 4 Hz and a wavelength of 0.1 m. What is the speed of the wave? ��Answer:

Wave Speed

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2. A motorboat is tied to a dock with its motor running. The spinning propeller makes a surface wave in the water with a frequency of 4 Hz and a wavelength of 0.1 m. What is the speed of the wave? ��Answer: ��The speed is 0.1 m × 4 Hz = 0.4 m/s

Wave Speed

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3. What is the speed of a wave in a spring if it has a wavelength of 10 cm and a period of 0.2 s? �����Answer: �

Wave Speed

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3. What is the speed of a wave in a spring if it has a wavelength of 10 cm and a period of 0.2 s? �����Answer: ��The speed is 10 cm/0.2 s = 50 cm/s

Wave Speed

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4. What is the wavelength of an earthquake wave if it has a speed of 5 km/s and a frequency of 10 Hz? ��Answer: ��

Wave Speed

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4. What is the wavelength of an earthquake wave if it has a speed of 5 km/s and a frequency of 10 Hz? ��Answer: ��The wavelength is (5 km/s)/10 Hz = 0.5 km.

Wave Speed

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The speed of a wave can change if it enters a new medium, or if variables such as pressure and temperature change.

For many kinds of waves, the speed of the waves is roughly constant for a range of different frequencies.

The wave with the lower frequency has a longer wavelength.

Wave Speed

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Amplitude

How is the amplitude of a wave related to the wave’s energy?

The amplitude of a wave is the maximum displacement of the medium from its rest position.

The more energy a wave has, the greater is its amplitude.

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The amplitude of a transverse wave is the distance from the rest position to a crest or a trough.

It takes more energy to produce a wave with higher crests and deeper troughs.

Amplitude

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The more energy a wave has, the greater is its amplitude.

Amplitude

Rest �position

High �amplitude

Low �amplitude

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The amplitude of a longitudinal wave is the maximum displacement of a point from its rest position.

The more energy the wave has, the more the medium will be compressed or displaced.

Amplitude

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  1. While wading in shallow waters, six waves crash into your legs in a 24-second span. What is the frequency of the waves?
    1. 4 Hz
    2. 18 Hz
    3. 0.25 Hz
    4. 2 Hz��

Assessment Questions

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  1. While wading in shallow waters, six waves crash into your legs in a 24-second span. What is the frequency of the waves?
    1. 4 Hz
    2. 18 Hz
    3. 0.25 Hz
    4. 2 Hz��ANS: C

Assessment Questions

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  1. What is the speed of an earthquake wave if it has a wavelength of 2.3 km and a frequency of 3 Hz?
    1. 6.9 km
    2. 5.3 km
    3. 6.0 km
    4. 1.3 km��

Assessment Questions

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  1. What is the speed of an earthquake wave if it has a wavelength of 2.3 km and a frequency of 3 Hz?
    1. 6.9 km
    2. 5.3 km
    3. 6.0 km
    4. 1.3 km��ANS: B

Assessment Questions

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  1. Which wave property increases as the energy of a wave increases?
    1. period
    2. frequency
    3. wavelength
    4. amplitude��

Assessment Questions

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  1. Which wave property increases as the energy of a wave increases?
    1. period
    2. frequency
    3. wavelength
    4. amplitude��ANS: D

Assessment Questions

17.2 Properties of Mechanical Waves