Why Frequency and Velocity Matter in Physics
Frequency is recognized as the fundamental characteristic of a wave. The definition of frequency is defined as the calculation (measurement) of the sum of waves that are passing through one point in a unit of time.
We also know what velocity is. In short, it is the rate of change of displacement. We need a brief explanation to state the term ‘velocity'—the total distance covered by a point. Within the same wave is called the velocity of the wave.
Here is the relation between velocity and frequency:
V = f × λ
Here,
V = velocity of the wave measure (using m/s).
f = frequency of the wave measured (using Hz).
λ = wavelength of the wave measured (using m).
Explanation on Relation Between Frequency Wavelength and Velocity
Do you know the characteristics of a wave? Wavelength, amplitude, frequency, and velocity- these four parameters are the characteristics. If a wave has a constant wavelength, you may notice the increment of velocity as well as frequency.
These three parameters are interdependent. Scientists have published many theorems and formulas based on the relation between wavelength frequency and velocity in particle physics.
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Let’s consider some examples which are related to the relation between frequency and wavelength and velocity:
When a particle is radiating a wave of constant wavelength, and the value of frequency is doubled, the radiated wave's velocity is also doubled .
When you notice a wave having a constant wavelength, and its frequency is four times its wavelength, then the velocity you observe is increased by four times.
Relation Between Speed and Frequency
Frequency is the total number of occurrences of a wave traveled in space (or vacuum) per unit of time. The unit for frequency is Hertz (Hz). Some common symbols are associated with frequency such as V and f.
The SI unit is Hz. S-1 is the SI base unit. The dimension for frequency is T1. The measurement of frequency is the total occurrences obtained due to a repeating wave per second.
The more is the period in the duration of time; the less will be the occurrences. Hence, occurrences and frequency both are reciprocal to each other.
To rectify any kind of oscillatory and vibratory phenomena, physicists use frequency at most. They use frequency to determine the calculation of mechanical vibrations, sound (audio signals), light, and radio waves.
Relationship Between Amplitude and Frequency
Although there is no direct relationship between frequency and amplitude or vice versa. Individually, they can be expressed by rearranging the terms of the wave equation.
Amplitude to Frequency Formula
The wave equation can be rearranged to express amplitude in terms of frequency and other variables.
\[A = y (t) sin (2\pi ft + \phi) \]
Frequency to Amplitude Formula
The wave equation can be rearranged to describe frequency in terms of amplitude and other variables.
\[f = sin - 1(y(t)A) - \phi 2 \pi t \]
Finding the Relation Between Frequency and Time
The number of cycles per unit time – the statement is used to define many cyclical processes. Those cyclical processes are waves, oscillation, frequency, and rotation, and so on. In particle physics, many physicists apply these terms to calculate certain values.
The relation between frequency and time is helping them quite enough to determine many requisite values for the benefits. Also, you will learn about frequency in optics, acoustics, and radio chapters from physics.
Frequency is denoted by a symbol (obtained from Latin letter) i.e. f
The relation between frequency and time is equal to f = 1/T
Before the invention of unit Hertz, physicists used the unit of cycles per second (cps) for frequency. This is a traditional unit of measurement. Engineers tried to calculate the frequency using certain mechanical devices.
Statistics Between Frequency and Period
Slower or longer waves are explained with the term ‘wave period’ (not frequency). Such waves are ocean surface waves. But waves like audio radio and light are expressed with the term ‘frequency’. These waves are faster and possess higher periods.
The table given below will show you the conversion of frequency to the period:
Mathematical Example: The sound produced by an object in the air has a wavelength of 20 cm. Find the object's frequency and period if the sound velocity in the air is 340 ms-1.
In this, Wave-length, γ = 20 cm = 0.2 m
Sound-velocity = 340 ms-1
Frequency, f =?
Period (time), T = ?
We know Velocity = fγ
So, f = v/γ = 340 ms-1 / 0.20 m = 1700 Hz
And T = 1/f = 1 / 1700 s-1
= 0.000588 s
= 5.88 x 10-4 s
Conclusion
Thank you for reading this article. We hope this article on Velocity and frequency was helpful for the students. You can also access sample papers, previous year papers, revision notes, and important questions from the website.
FAQs on Understanding the Relation Between Frequency and Velocity
1. What is the fundamental relationship between wave velocity, frequency, and wavelength?
The relationship is defined by the formula v = fλ, where 'v' represents the wave velocity, 'f' is the frequency, and 'λ' (lambda) is the wavelength. This equation shows that wave velocity is the product of its frequency and wavelength. For any wave travelling through a constant medium, its velocity is constant, which means its frequency and wavelength are inversely proportional.
2. What is frequency, and what is its standard unit of measurement?
Frequency is the measure of the number of complete wave cycles that pass a specific point per unit of time. It essentially describes how often a wave oscillates. The standard SI unit for frequency is the Hertz (Hz), where 1 Hz is equivalent to one cycle or one oscillation per second.
3. Does the relationship v = fλ apply to all types of waves?
Yes, the relationship v = fλ is a universal principle that applies to all forms of waves. This includes mechanical waves, such as sound waves and water waves, as well as electromagnetic waves like light, radio waves, and X-rays. While the velocity of the wave can change depending on the medium it travels through, the mathematical connection between its velocity, frequency, and wavelength remains constant.
4. Why is the relationship between frequency and velocity important in real-world applications?
This relationship is crucial across many scientific and technological fields. For instance:
- In telecommunications, it allows engineers to manage the broadcast spectrum for radio, TV, and mobile phones by assigning specific frequencies.
- In medical imaging, ultrasound machines use high-frequency sound waves (and thus short wavelengths) to create detailed images of internal body parts.
- In astronomy, analysing the frequency of light from distant stars helps determine their motion and composition.
5. If a wave moves from one medium to another, like light from air to water, which of its properties change?
When a wave crosses the boundary between two different media, its frequency remains constant. This is because the frequency is determined by the wave's source. However, the wave's velocity changes because the new medium has different physical properties. To satisfy the equation v = fλ, if the velocity (v) changes and frequency (f) stays the same, the wavelength (λ) must also change.
6. How is frequency (f) different from angular frequency (ω)?
Frequency (f) measures the number of cycles per second and is expressed in Hertz (Hz). In contrast, angular frequency (ω) measures the rate of angular displacement, or rotation, in radians per second. They describe the same oscillatory motion but use different units. The two are directly related by the formula ω = 2πf. Angular frequency is often used when describing rotational systems or simple harmonic motion.
7. Does changing the amplitude of a wave affect its velocity?
No, changing the amplitude of a wave does not affect its velocity. The velocity of a wave is determined by the properties of the medium it is travelling through. Amplitude is related to the energy carried by the wave—a higher amplitude signifies higher energy, but the speed at which the wave propagates remains independent of it.
8. What happens to a wave's velocity if its frequency is doubled while its wavelength is held constant?
According to the wave equation v = fλ, the velocity of a wave is directly proportional to both its frequency and wavelength. If you double the frequency (f) while keeping the wavelength (λ) constant, the wave's velocity (v) will also double. However, it's important to note that this scenario is theoretical, as in a given medium, changing the frequency of a wave source would typically cause a corresponding change in wavelength, keeping the velocity constant.
