Ripples in water, sound traveling in air, and coordinated vibrations of objects are examples of waves you have probably encountered in your life. A good way to visualize a wave is to insert the end of a pencil into a container of still water. The surface of the water is disturbed, producing ripples, or waves.
Electromagnetic waves are special waves, such as light, radio waves, microwaves, and x-rays, that do not require a medium for propagation. We cannot see or hear these waves, but they exist in nature and in many of the products we use every day.
Regardless of the kind, every wave has a wavelength. Wavelength is the distance between two successive like points on a wave. Some examples are the distance between two adjacent peaks or two adjacent valleys. A peak is the highest point of a wave and a valley is the lowest point of a wave. Stated another way, wavelength is the time required to complete one full cycle of the wave.
Wavelength depends on two other important parameters:
1. Wave Speed
The rate at which the wave moves through the medium of propagation. Wave speed is dependent upon the medium of propagation. For example, water ripples travel through the water. Electromagnetic waves usually travel through the air, as do sound waves. Vibrations on a piano string travel through the string. The wave speed is different for all of these because the medium in which the wave propagates is different.
The number of wave cycles passing a point per unit time. Stated another way, it is the number of oscillations per second in the wave. A higher frequency means a shorter wavelength, and a shorter wavelength means a higher frequency. This leads us to the relationship between wave speed, frequency, and wavelength.
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The speed of the wave equals the number of cycles passing a point each second multiplied by the cycle length.
Mathematically stated: wave speed = cycles per second x cycle length
Wave speed is represented by the variable v, frequency (cycles per second) by f, and wavelength (cycle length) by the Greek letter λ. So v = f * λ or solving for λ, the equation becomes λ = v / f.
Wave speed has units of distance per unit time, for example, meters per second or m/s. Frequency has units of Hz. Wavelength is measured in units of distance, usually meters (m).
Let's try some examples. Find the wavelength of the radio waves produced by an AM radio station transmitting at 770 kHz.
The AM radio station is transmitting radio waves into the air. Electromagnetic waves travel through air at approximately the speed of light in a vacuum (which is approximately 300,000,000 m/s). Therefore, we have:
λ= 300,000,000 / 770,000 = 390 m.
The middle C musical note has a frequency of 261.6 Hz. Calculate the wavelength of the sound of the note in air at room temperature. The speed of sound in air at room temperature is approximately 344 m/s. So:
λ= 344 / 261.6 = 1.31 m.
Wavelength is an important parameter of waves and is the distance between two like points on the wave. The wavelength is calculated from the wave speed and frequency by λ = wave speed/frequency, or λ = v / f. A peak is the highest point of a wave, while the valley is the lowest point of a wave. Wave speed is the rate at which the wave moves through the medium of propagation, and frequency is the number of wave cycles passing a point per unit time. The wave speed depends on the medium in which the wave propagates. As wavelength increases, frequency decreases, and as frequency increases, wavelength decreases.
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Wavelength exists in different products and applications we use in our everyday lives such as microwaves, the radio, and how we see and interpret colors. The problems below will assist you in calculating the wavelength from different scenarios and sets of information. Wavelength can be determined based on its relationship with frequency and wave speed. The solutions are provided in order to further understand the calculations step by step.
1. Calculate the wavelength of a sound wave that has a frequency of 110 Hz and a wave speed of 160,000 m/s.
2. What is the wavelength of an unidentified wave that has a wave speed of 50 m/s and a frequency of 15 kHz?
3. The wavelength of a specific note in a song played on the radio was 190 m. The frequency was determined to be 1500 Hz. What is the wave speed of this note?
4. Determine the wavelength of a wave based on the parameters provided. The wave has a frequency of 190 kHz and a wave speed of 5,000,000 m/s.
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How to Calculate Wavelength
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