Frequency Formula (f = 1 / T)
The frequency formula is a fundamental concept in physics that calculates the number of complete cycles, waves, or oscillations occurring per unit of time. It is a highly tested concept in CBSE board exams, JEE, and NEET across topics like Waves, Sound, Optics, and Alternating Current.
Class: 9, 11 & 12
Topic: Waves & Oscillations
Exams: CBSE · JEE · NEET
What is Frequency?
In physics, frequency is defined as the number of occurrences of a repeating event per unit of time. For a wave (like sound or light) or a simple pendulum, it represents the number of cycles completed in one second. It is universally denoted by the letter f or the Greek letter nu (ν).
✓ Quick read
If a heart beats 72 times in 60 seconds, its frequency is 72/60 = 1.2 beats per second. You don't need complex math—just the total events divided by total time!
1. Frequency Formula in terms of Time Period
The most basic formula links frequency directly to the Time Period (T). The time period is the duration taken for exactly one complete cycle. The relationship is inversely proportional.
Frequency & Time Period
f = 1T
Here:
- f = Frequency (in Hertz, Hz)
- T = Time Period (in seconds, s)
2. Frequency Formula in terms of Wavelength & Wave Speed
When studying wave propagation, frequency is calculated using the wave's velocity and its wavelength. This formula is critical for optics and acoustics problems.
Wave Frequency Formula
f = vλ
Here:
- f = Frequency (Hz)
- v = Speed or velocity of the wave (m/s)
- λ (Lambda) = Wavelength (m)
3. Angular Frequency Formula
In circular motion or simple harmonic motion (SHM), objects rotate or oscillate through angles. Here we use Angular Frequency (ω), which measures angular displacement per unit of time.
Angular to Linear Frequency
f = ω2π
Where ω is measured in radians per second (rad/s).
4. Frequency of a Photon (Quantum Physics)
In Modern Physics (Class 12), the frequency of an electromagnetic wave/photon is derived from Planck's Equation relating to the energy of the photon:
E = hνPlanck's equation where h is Planck's constant.
f (ν) = EhRearranged for frequency.
Units & Dimensional Formula
Keeping track of units is essential to avoid negative marking in competitive exams.
| Quantity |
Value / Details |
| S.I. Unit |
Hertz (Hz) or s-1 |
| C.G.S Unit |
Cycles per second (cps) |
| Dimensional Formula |
[M0 L0 T-1] |
Common Mistakes to Avoid
× Unit Mismatch for Wavelength
When using f = v / λ, students often forget to convert wavelength into meters. If wavelength is given in Nanometers (nm), multiply by 10-9. If given in Angstroms (Å), multiply by 10-10 before calculating.
× Confusing ω with f
Angular frequency (ω) and standard frequency (f) are different! Angular frequency is measured in rad/s, while standard frequency is in Hz. Always use f = ω / 2π to convert between them.
Solved Examples on Frequency Formulas
Example 1
A simple pendulum completes one oscillation in 0.2 seconds. Calculate its frequency.
Given, Time Period (T) = 0.2 s
Formula used: f = 1 / T
f = 1 / 0.2 = 5
Frequency (f) = 5 Hz
Example 2
A sound wave travels through air at 340 m/s and has a wavelength of 1.7 meters. What is the frequency of the sound?
Given, Velocity (v) = 340 m/s, Wavelength (λ) = 1.7 m
Formula used: f = v / λ
f = 340 / 1.7 = 200
Frequency (f) = 200 Hz
Example 3
The angular frequency of an alternating current (AC) generator is 314 rad/s. Find its standard frequency. (Use π = 3.14)
Given, Angular frequency (ω) = 314 rad/s
Formula used: f = ω / 2π
f = 314 / (2 × 3.14) = 314 / 6.28 = 50
Frequency (f) = 50 Hz
Practice Questions
Try these on your own to strengthen your understanding of the topic:
- A tuning fork vibrates 512 times in 2 seconds. What is its frequency? (Ans: 256 Hz)
- Light waves travel at a speed of 3 × 108 m/s. If the wavelength of red light is 600 nm, find its frequency. (Ans: 5 × 1014 Hz)
- A particle undergoing SHM has a time period of 0.04 seconds. Calculate its angular frequency (ω). (Ans: 50π rad/s)
Frequently Asked Questions
What is the frequency formula?
The primary frequency formula is f = 1 / T, which states that frequency is the reciprocal of the time period. Another common formula is f = v / λ for calculating wave frequency.
What is the relationship between frequency and wavelength?
Frequency and wavelength are inversely proportional to each other, assuming the speed of the wave remains constant. When the wavelength is long, the frequency is low, and vice versa.
What is the dimensional formula of frequency?
Because frequency is defined as cycles per second (1 / Time), its dimensional formula is [M0 L0 T-1].
Can frequency ever be negative?
No, physical frequency cannot be negative. It is a scalar quantity that counts the number of times an event happens, which can only be zero or a positive number.
What is the S.I unit of frequency?
The standard S.I. unit of frequency is the Hertz (Hz), which is equivalent to one complete cycle or oscillation per second.