# Frequency, Hertz, and Waves

Updated on October 15, 2012

## By Joan Whetzel

Frequency, commonly associated with the measurement of sound waves, can be visualized clearly on an oscilloscope. This scientific instrument shows the wavelength and the amplitude of each wave of sound. Of course, sound is not the only thing that produces waves; light produces waves as well. Frequency is used to measure both sound and electromagnetic radiation waves.

What Is Frequency?

Frequency measures the repetitive occurrence of an event, in other words it measures regularly occurring cycles over a specific time frame. Hertz is the standard measurement used for frequency; 1 Hertz (Hz) equals 1 cycle per second. In essence, each Hz is measuring the space between waves. The intensity of that sound (the pitch) is found by measuring the amplitude (height) of the waves in decibels (dB).

Frequency can be converted from Hz (cycles per second for sound) to angular velocity (which measures angular displacement in connection with time, or the speed at which something moves along a circular path) and rotational speed (which measures rotations or revolutions in a specific time frame, or how long it takes an object to make a complete revolution). For example, if a runner takes 1 minute to make one lap around a track measuring 1/4 mile in length, the runner's rotational speed is 1 lap per minute (1/4 mile per minute). Since 1/4 mile is equivalent to 1,320 feet and that minute breaks down into 60 seconds, the runners angular velocity can be figured as follows: 1,320 feet ÷ 60 seconds, which equals an angular velocity of 220 feet per second.

Hertz Explained

Hertz is used to measure the frequency of sound waves as well as electromagnetic waves (light and radio waves). Since Hz is the SI unit for cycles per second, the frequency can be found by choosing a time frame (second, minute, hour) and measuring how many cycles occur during that time frame. The base measurement is 1 Hz which is equal to 1 cycle per 1 second. Adding a prefix to the Hertz provides a range of measurements from the tiniest fraction of a cycle per second to the largest cycle imaginable.

Electrical signals and sound waves range from the smallest fraction of a Hz to thousands or millions of Hertz. For instance, 1billion nanohertz equals 1 Hz whereas 1 Hz equals 0.000000001 nanohertz. One petrahertz is equivalent to 1 quadrillion Hz and 1 Hertz is equal to 0.000000000000001 petrahertz. The prefix determines how to multiply or divide the Hz.

The nanohertz works out to be an extremely slow frequency dragging its feet at 1 billionth of a cycle per second, so a billion seconds have to pass between cycles. That works out to 277,777.78 hours, or about 31.7 years between cycles. The petrahertz, on the other hand is extremely fast, whizzing by a breakneck speed of a quadrillion cycles per second.

The "A" above middle "C", in music, has a frequency of 440 Hz. The lowest "A" on the piano keyboard has a frequency of 110 Hz and the highest "A" on the keyboard as a frequency of 7040 Hz.

Using Hertz to Determine Angular Velocity and Rotational Speed

Angular velocity is measured in radians or degrees per minute and rotational speed is generally measured in cycles per second or revolutions per 60 seconds / 1 minute. So converting from a frequency speed of, say, 10 Hertz to Angular Velocity or Rotational Speeds involves the following equations:

· Radians: 10 cycle per second x 6.26 radians per second = 62.6 radians per second

· Degrees: 10 cycles per second x 360 degrees per second = 3,600 degrees per second

· Revolutions : 10 cycles per second x 1 cycle per second = 10 cycles per second

Bibliography

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http://tf.nist.gov/general/enc-f.htm

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