Physics Formula Waves
Physics Formulas for Waves
Waves are disturbances that transfer energy from one point to another without transferring matter. They can be categorized into mechanical waves, which require a medium to travel through, and electromagnetic waves, which can travel through a vacuum.
Key Formulas for Waves
1. Wave Speed (v)
The speed of a wave is given by:
\[ v = f \lambda \]
where:
- \( v \) is the wave speed.
- \( f \) is the frequency of the wave.
- \( \lambda \) is the wavelength of the wave.
2. Frequency (f)
The frequency of a wave is the number of wave cycles that pass a given point per unit of time:
\[ f = \frac{1}{T} \]
where:
- \( f \) is the frequency.
- \( T \) is the period of the wave (the time it takes for one complete wave cycle).
3. Wavelength (λ)
The wavelength is the distance between successive crests (or troughs) of a wave:
\[ \lambda = \frac{v}{f} \]
where:
- \( \lambda \) is the wavelength.
- \( v \) is the wave speed.
- \( f \) is the frequency.
4. Period (T)
The period of a wave is the time taken for one complete cycle of the wave to pass a given point:
\[ T = \frac{1}{f} \]
where:
- \( T \) is the period.
- \( f \) is the frequency.
5. Energy of a Photon (E)
For electromagnetic waves (such as light), the energy of a photon is given by:
\[ E = h f \]
where:
- \( E \) is the energy.
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) Js).
- \( f \) is the frequency.
Example Problems
Example 1: Calculating Wave Speed
A wave has a frequency of 5 Hz and a wavelength of 3 meters. What is the speed of the wave?
Using the wave speed formula:
\[ v = f \lambda \]
\[ v = 5 \, \text{Hz} \times 3 \, \text{m} = 15 \, \text{m/s} \]
The speed of the wave is 15 meters per second.
Example 2: Finding the Frequency
A wave travels at a speed of 340 m/s and has a wavelength of 2 meters. What is its frequency?
Using the wavelength formula:
\[ f = \frac{v}{\lambda} \]
\[ f = \frac{340 \, \text{m/s}}{2 \, \text{m}} = 170 \, \text{Hz} \]
The frequency of the wave is 170 Hz.
Example 3: Determining the Wavelength
A sound wave has a frequency of 256 Hz and travels at a speed of 343 m/s. What is its wavelength?
Using the wavelength formula:
\[ \lambda = \frac{v}{f} \]
\[ \lambda = \frac{343 \, \text{m/s}}{256 \, \text{Hz}} \approx 1.34 \, \text{m} \]
The wavelength of the sound wave is approximately 1.34 meters.
Example 4: Calculating the Energy of a Photon
A photon has a frequency of \( 6 \times 10^{14} \) Hz. What is its energy?
Using the photon energy formula:
\[ E = h f \]
\[ E = 6.626 \times 10^{-34} \, \text{Js} \times 6 \times 10^{14} \, \text{Hz} \]
\[ E \approx 3.98 \times 10^{-19} \, \text{J} \]
The energy of the photon is approximately \( 3.98 \times 10^{-19} \) joules.
Summary
- Wave speed is the product of frequency and wavelength.
- Frequency is the inverse of the period.
- Wavelength is the distance between successive wave crests or troughs.
- Period is the time for one complete wave cycle.
- The energy of a photon is proportional to its frequency.
These fundamental wave formulas are essential in various physics applications, from sound waves to electromagnetic waves like light.
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