Question

What are the units for wavelength and frequency of electromagnetic waves? What is the speed of light in meters per second and miles per hour?

Short answer

Wavelength is measured in meters; frequency in hertz. The speed of light is about 299,792,458 m/s or 670,616,629 mph.

Step-by-step solution

Understand the Concept of Wavelength and Frequency

Wavelength and frequency are properties of electromagnetic waves. Wavelength is the distance between consecutive crests (or troughs) of a wave, while frequency is the number of waves that pass a point in one second. Both terms are fundamental concepts in physics.

Units of Wavelength

The wavelength of electromagnetic waves is typically measured in meters (m). However, depending on the type of electromagnetic wave (e.g., radio waves, visible light, etc.), wavelengths can also be expressed in nanometers (nm), micrometers (µm), or other length units.

Units of Frequency

Frequency is measured in hertz (Hz), where 1 Hz is equal to one cycle per second. In terms of measurement, frequency indicates how many complete wave cycles occur in one second.

Speed of Light in Meters Per Second

The speed of light in a vacuum is a constant and is approximately 299,792,458 meters per second (m/s). This value is often rounded to 3 × 10^8 m/s for simplicity in calculations.

Convert Speed of Light to Miles Per Hour

To convert the speed of light from meters per second to miles per hour, use the conversion factors: 1 meter = 0.000621371 miles and 1 hour = 3600 seconds. Thus, the speed of light in miles per hour can be calculated as follows:\[ 299,792,458 ext{ m/s} imes 0.000621371 ext{ miles/m} imes 3600 ext{ seconds/hour} = 670,616,629 ext{ miles per hour} \]

Key concepts

Understanding Units of Wavelength

Wavelengths are essential for identifying the characteristics of electromagnetic waves. The most standard unit for measuring wavelength is the meter (m), which accommodates a wide range of applications. However, different fields and types of electromagnetic waves may require more specific measurements:

• Nanometers (nm) - often used when dealing with visible light. 1 nm is equal to 10^-9 meters.
• Micrometers (µm) - handy for infrared waves. 1 µm is equal to 10^-6 meters.
• Millimeters (mm) - generally used in the context of radio waves. 1 mm equals 10^-3 meters.

Choosing the right unit helps in accurately describing the wave, based on its usage or scientific requirement.

Comprehending Units of Frequency

Frequency tells us how often a wave oscillates per second and is key in understanding wave behavior. The fundamental unit of frequency is the hertz (Hz):

• 1 Hertz (Hz) signifies one complete wave cycle per second.
• Kilohertz (kHz) represents 1,000 cycles per second, often used in radio broadcasting.
• Megahertz (MHz) corresponds to 1,000,000 cycles per second and is used for television broadcasts and microwaves.
• Gigahertz (GHz) is 1,000,000,000 cycles per second, utilized in modern communications technology like Wi-Fi.

Different contexts require different frequency units, making it a versatile measurement in wave analysis.

Speed of Light in Meters Per Second

In physics, the speed of light is a critical constant denoting how fast light travels in a vacuum. This speed is approximately 299,792,458 meters per second (m/s). It is so pivotal that scientists often use the rounded value of 3 × 10⁸ m/s to simplify calculations without significantly affecting accuracy. This constant speed is the foundation for many equations and laws in physics, especially in relativity theory and electromagnetic theory.

Conversion of Speed of Light to Miles Per Hour

While the metric system is extensively used in scientific contexts, converting the speed of light to miles per hour can be useful, especially in applications involving speed comparisons over long distances. To perform this conversion:

• Firstly, note that 1 meter is equivalent to 0.000621371 miles.
• Also, there are 3,600 seconds in an hour.

Therefore, when translated to miles per hour, the speed of light is calculated as follows:\[ 299,792,458 \text{ m/s} \times 0.000621371 \text{ miles/m} \times 3600 \text{ seconds/hour} = 670,616,629 \text{ miles per hour} \]This massive number illustrates the incredible speed at which light can travel long distances in a blink of an eye.