Problem 3
Question
Traffic signals are often now made of LEDs (lightemitting diodes). Amber and green ones are pictured here. (a) The light from an amber signal has a wavelength of \(595 \mathrm{nm},\) and that from a green signal has a wavelength of 500 nm. Which has the higher frequency? (b) Calculate the frequency of amber light. (IMAGE CAN'T COPY)
Step-by-Step Solution
Verified Answer
(a) Green light has the higher frequency. (b) Amber light's frequency is approximately \(5.04 \times 10^{14}\) Hz.
1Step 1: Understand the Relationship Between Wavelength and Frequency
The frequency \(f\) and wavelength \(\lambda\) of light are related by the equation \( c = \lambda f \), where \(c\) is the speed of light in a vacuum, approximately \(3.00 \times 10^8\) meters per second. This equation tells us that as the wavelength decreases, the frequency increases and vice versa.
2Step 2: Compare Wavelengths to Determine Which Has Higher Frequency
Given that the amber light has a wavelength of 595 nm and the green light has a wavelength of 500 nm, the green light has a shorter wavelength. Since frequency and wavelength are inversely related, the green light has a higher frequency than the amber light.
3Step 3: Convert Wavelength from Nanometers to Meters for Calculation
To find the frequency, convert the wavelength from nanometers to meters. For amber light, \( 595 \text{ nm} = 595 \times 10^{-9} \text{ m} \).
4Step 4: Calculate the Frequency of Amber Light
Use the formula \( f = \frac{c}{\lambda} \) to calculate the frequency. Substitute \( c = 3.00 \times 10^8 \text{ m/s} \) and \( \lambda = 595 \times 10^{-9} \text{ m} \):\[ f = \frac{3.00 \times 10^8}{595 \times 10^{-9}} \approx 5.04 \times 10^{14} \text{ Hz} \]
Key Concepts
Wavelength and FrequencySpeed of LightLED Light Properties
Wavelength and Frequency
In the world of physics, light exhibits both wave-like and particle-like properties. Two key aspects of light waves are their wavelength and frequency. Wavelength is the distance between two consecutive peaks of a wave and is usually measured in nanometers (nm). Frequency, denoted as \(f\), refers to how many wave cycles occur per second and is measured in hertz (Hz).
There's a vital relationship between wavelength and frequency given by the formula: \( c = \lambda f \), where \(c\) is the speed of light in a vacuum. Essentially, this equation tells us that as the wavelength \(\lambda\) of light decreases, its frequency \(f\) increases. This relationship is described as inversely proportional.
Consider amber and green light. Amber light has a wavelength of 595 nm, whereas green light has a shorter wavelength of 500 nm. Since a shorter wavelength corresponds to a higher frequency when speeds are constant, green light naturally has a higher frequency than amber light.
There's a vital relationship between wavelength and frequency given by the formula: \( c = \lambda f \), where \(c\) is the speed of light in a vacuum. Essentially, this equation tells us that as the wavelength \(\lambda\) of light decreases, its frequency \(f\) increases. This relationship is described as inversely proportional.
Consider amber and green light. Amber light has a wavelength of 595 nm, whereas green light has a shorter wavelength of 500 nm. Since a shorter wavelength corresponds to a higher frequency when speeds are constant, green light naturally has a higher frequency than amber light.
Speed of Light
The speed of light, denoted as \(c\), is a fundamental constant in physics. It describes how fast light travels in a vacuum, which is approximately \(3.00 \times 10^8\) meters per second. This immense speed allows light to travel around the Earth nearly seven and a half times in just one second!
The speed of light is crucial for calculations involving the properties of light, such as wavelength and frequency. It serves as the constant connector between frequency and wavelength in the equation \( c = \lambda f \). When calculating frequency \(f\), we can simply rearrange the formula to \( f = \frac{c}{\lambda} \).
Using this, we can find the frequency of a given light by knowing its wavelength. For instance, for amber light with a wavelength of 595 nm, after converting it into meters \((595 \times 10^{-9}\) meters), we can calculate its frequency \(f\) as approximately \(5.04 \times 10^{14}\) Hz.
The speed of light is crucial for calculations involving the properties of light, such as wavelength and frequency. It serves as the constant connector between frequency and wavelength in the equation \( c = \lambda f \). When calculating frequency \(f\), we can simply rearrange the formula to \( f = \frac{c}{\lambda} \).
Using this, we can find the frequency of a given light by knowing its wavelength. For instance, for amber light with a wavelength of 595 nm, after converting it into meters \((595 \times 10^{-9}\) meters), we can calculate its frequency \(f\) as approximately \(5.04 \times 10^{14}\) Hz.
LED Light Properties
LEDs, or light-emitting diodes, are common in modern lighting because they are efficient and versatile. They consume less power and can emit a range of light colors based on their semiconductor properties.
The color of light from an LED is due to the wavelength of light it emits. For instance, amber LEDs emit light with wavelengths around 595 nm, while green LEDs emit around 500 nm. The varying wavelengths mean that each color of light has different frequencies and energy levels. LEDs can be precisely tuned to produce specific wavelengths, leading to their use in various applications from traffic signals to display screens.
LEDs are advantageous because they convert electricity directly into light with minimal energy lost to heat. They provide a controlled and steady source of light, which is why you see them used in critical and high-visibility applications like traffic signals.
The color of light from an LED is due to the wavelength of light it emits. For instance, amber LEDs emit light with wavelengths around 595 nm, while green LEDs emit around 500 nm. The varying wavelengths mean that each color of light has different frequencies and energy levels. LEDs can be precisely tuned to produce specific wavelengths, leading to their use in various applications from traffic signals to display screens.
LEDs are advantageous because they convert electricity directly into light with minimal energy lost to heat. They provide a controlled and steady source of light, which is why you see them used in critical and high-visibility applications like traffic signals.
Other exercises in this chapter
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