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Relation between Frequency and Wavelength can be shown by the following formula, λ = cf.
Where,
- λ = wavelength of the wave
- C = speed of the wave in the given medium
- f = frequency of the wave
In a medium, energy is carried by a disturbance or by a vibration called a wave without a net movement of particles in that medium. Waves are crucial for the transfer of energy and it follows a periodic motion.
- Frequency can be defined as the number of cycles or turns that are made per second by an alternating quantity.
- Period (T) can be expressed as the reciprocal of the frequency and vice versa.
- While, a Wavelength is the distance between each repeated wave in both the case of Longitudinal and Transverse waves.
Read Also: NCERT Solutions for Class 11 Physics Waves
| Table of Content |
Key Terms: Waves, Wavelength, Frequency, Amplitude, Energy, Temperature, Magnetic Intensity, Transverse Waves, Longitudinal Waves
What are Waves?
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A wave can be defined as:
| “A form of disturbance in a medium which carries energy without a net particle movement.” |
- A wave can take the form of a pressure variation, elastic deformation, electric potential, temperature and electric or magnetic intensity.
- Waves help in the transfer of energy.
- The movement of waves involves periodic and repetitive.
- Waves do not result in a net movement of the medium or particles in the medium (which is the mechanical wave).
Check More:
| Related Articles | ||
|---|---|---|
| Wave Power | Wave Nature of Electromagnetic Radiation | Gravity Waves |
| Interference of Waves | Difference between Transverse and Longitudinal Waves | Ground Wave propagation |
Types of Waves
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There are different types of waves in nature:
- Transverse Waves: In these waves, the medium moves at a 90° to the direction of the wave. Water Waves, Light waves, and S-Wave, come under Transverse waves where the highest point of the wave is Crest and the lowest point is the Trough.
- Longitudinal Waves: In longitudinal waves, the particles move in the same dimension as the movement of waves in the medium. Sound waves, and P-Waves come under Longitudinal Waves where the wave forms two regions.
Transverse and Longitudinal waves
- Surface Waves: In this type of wave, when particle movement occurs along the direction of the movement of energy in a medium with a circular motion. For instance: Seismic Waves, Electromagnetic Waves
A wave has two major components: Frequency and Amplitude which defines different characteristics of a wave and helps to understand the nature of a wave. It has a set of positive values and a set of negative values that alternates with each other and it goes through a complete 360° electrical cycle and is hence completing one cycle.
| 1 cycle = 1 positive half + 1 negative half |
What is Frequency?
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Frequency is defined as the number of cycles or turns made per second made by an alternating quantity. The period can be expressed as the reciprocal of the frequency and vice versa. Thus,
| \(\begin{array}{l}Period = \frac{1}{Frequency}\end{array}\) or \(\begin{array}{l}Frequency= \frac{1}{Period}\end{array}\) |
- The frequency of a wave can be defined as the number of waves that pass a point in a certain time.
- The unit of frequency is hertz (Hz) and is equivalent to one wave per second.
- Frequency can be denoted by (f).
- For example, if a wave completes two cycles in 1 second. So we can say that the frequency of the wave is 2 Hertz. It can be calculated as: Frequency = Total Number of cycle (N) per Second (sec).
- Frequency can also be defined as the Number of Oscillations or Turns per second or how frequently the particles present in a medium vibrate when a wave propagates through the medium.
Frequency and Wavelength Relationship Infographic
Read Also: Brewster’s Law Formula
What is Wavelength?
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Wavelength is defined as the length between two consecutive Troughs or two consecutive crests. Wavelength can also be expressed as the distance between each repeated wave in both the case of Longitudinal and Transverse waves.
- Thus, two adjacent peaks or troughs on a wave have been separated by a distance of a single complete wavelength.
- The letter lambda (λ) represents the wavelength of a wave.
- In the case of a longitudinal wave, the wavelength is the distance between the two consecutive compressions or between the two consecutive rarefactions.
- In case of a Transverse wave, it is the distance between the two consecutive troughs or crests formed by the wave.
- Wavelength is denoted by Lambda (λ) and expressed in metres (m).
Wavelength
Read More: Waves Important Questions
Formula for Wavelength to Frequency
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The wavelength-to-frequency formula can be represented as:
| Speed = Frequency x Wavelength |
Thus, \(Wavelength = \frac{(Speed\ of \ Wave)}{(Frequency\ of\ Wave)}\)
As per the above formula, the representation of all the quantities is by a symbol. The symbolic representation can be shown as:
⇒ C = f × λ
As per wavelength to frequency, the expression of the formula can be denoted as:
⇒ λ = cf
Here,
- λ = wavelength of the wave
- C = speed of the wave in the given medium
- f = frequency of the wave
Difference between Frequency and Wavelength
The difference between Frequency and Wavelength is:
| Frequency | Wavelength |
|---|---|
| Frequency is the number of complete wave cycles per second. | Wavelength is the total distance covered to complete one wave. |
| Helps to determine Time. | Helps to determine Distance. |
| It is indicated by the symbol f. | It is indicated by the symbol λ. |
| Here, f = c/λ is the formula that helps to calculate frequency (c is the speed of light). | Here, λ = c/f is the formula that helps to calculate wavelength (c is the speed of light). |
| The SI unit of frequency is Hertz (Hz). | The SI unit of Wavelength (λ) is meter (m). |
| Frequency can be used to find the recurrence of sound waves. | Wavelength can be used to determine the length of sound waves. |
Relation Between Frequency and Wavelength
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The wavelength of a wave and the Frequency of a wave is inversely related. When there is a long wavelength, the frequency is low, but in case of a short wavelength, the frequency is high.
Period (T) is another quantity that can be used to express a wave. A Period (T) can be defined as the time taken to complete one oscillation. It is because frequency helps to determine the number of times a wave oscillates and it can be expressed as,
f = 1 / t
Every point on the wave returns to the same value after one period, since a wave undergoes one oscillation during one period. This occurs as a result of every session of oscillation travelling a distance of a wavelength in one period to finish. The wave speed (v) is defined as the distance travelled by a wave per unit of time. If considered that the wave travels a distance of one wavelength in one period,
ν = λ/T
As we know that T = 1/f, hence we can express the above equation as,
V = f λ
The wave speed is equal to the product of its frequency and wavelength, and this implies the wavelength and frequency relationship.
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Things to Remember
- There are different frequencies of waves present in our environment. And not all frequencies are audible to a human ear.
- For a human ear the sound frequency ranges from 20 Hz- 20,000 Hz, hence it is the audible range of sound for humans.
- Sound with Frequencies less than the audible range is known as Infrasound and more than the audible range is known as Ultrasound.
- The SI unit of Wavelength (λ) is meter (m).
- The SI unit of frequency is Hertz (Hz).
Read Also: Transverse and Longitudinal Waves
Previous Years Questions
- The emission of photoelectrons is directly proportional to…. [NEET 1997]
- If the kinetic energy of the particle is increased to 16 times its previous value… [KEAM]
- The de-Broglie wavelength associated with the electrons would be… [ NEET 2011]
- If its disintegration constant is 3.7×104sec−1, the mass…. [ AP EAPCET 1998 ]
- When monochromatic radiation of intensity II falls on a metal surface…. [NEET 2010]
- An example for the best source of monochromatic light is… [JKCET 2019]
- The wavelength of a 1 keV photon is 1.24 nm… [KEAM]
- By photoelectric effect, Einstein proved…. [NEET 2000]
- The energy of most energetic photoelectron is…. [JIPMER 1999]
- In a photoelectric experiment, if both the intensity and frequency of the incident… [KEAM]
Sample Questions
Ques. What is the relation between Frequency and Temperature? (1 mark)
Ans. Frequency and Temperature are directly related as when the temperature increases, the frequency also increases.
Ques. How Infrared waves are produced? (1 mark)
Ans. Infrared waves are included under higher wavelengths and are produced by hot bodies and materials as their primary source is thermal radiation or heat. They have low frequency and are towards the end of the visible spectrum. These waves are used in medical applications, industrial involvement and in other technical equipment.
Ques. How Bats can fly in the dark? (1 mark)
Ans. Bats can produce ultrasonic waves of range 20k Hz to 200 kHz which is not audible for human eyes. They produce these by contracting their voice box (Larynx) and throw this wave in front of them while flying. If there is a reflection of waves, then this indicates that there is some obstacle in their path and in this way they are able to fly in the dark.
Ques. Determine the wavelength of a wave travelling at 100 m/s at a frequency of 11 Hz? (2 marks)
Ans. By using the formula,
\(\lambda = c/f\)
Thus,
= 100/11 = 9.09 m
Ques. What is the frequency of a tuning fork whose time period is 0.05s? (2 marks)
Ans. We know the relation between frequency and time period as:
\(\text{Frequency} = \frac{1}{\text{Time Period}}\)
Frequency = 1/ 0.05
= 100/5
= 20 Hz.
Ques. Does Temperature have an effect on Wavelength? (2 marks)
Ans. Yes, Temperature has an inverse effect on Wavelength. The frequency at which an electron oscillates is set by the temperature of the matter in which the electron stays or resides. Lower temperature produces lower frequency and we can say that at low frequency the wavelength of the radiation is also long.
But when the temperature increases, the rate of oscillations becomes faster and leads to higher oscillation frequency. This high frequency means that the radiation has a comparatively shorter wavelength.
Ques. A clinic uses an ultrasonic scanner machine to locate the tumours present in human tissue. What is the wavelength of sound in the tissue in which the speed of sound is 1.7 km/s? The operating frequency of the scanner machine is 4.2 MHz. (2 marks)
Ans. The speed of sound (v)= 1.7 km/s= 1.7 × 103 m/s
Frequency of the scanner (f)= 4.2 MHz= 4.2 × 106 Hz
\(\text{Wavelength} = \frac{\text{Velocity of Wave}}{\text{Frequency}}\)
\(\lambda = \frac{v}{f}\)
= (1.7 × 103 m/s)/ 4.2 × 106 Hz
= 4.1 × 10-4 m
Ques. A sound wave is travelling with a velocity of 360m/s and has a frequency of 1200 Hz. What is its wavelength? (2 marks)
Ans. The speed of sound (v)= 360 m/s
Frequency of the scanner (f)= 1200 Hz
\(\text{Wavelength} = \frac{\text{Velocity of Wave}}{\text{Frequency}}\)
\(\lambda = \frac{v}{f}\)
= 360m/sec / 1200Hz
= 0.3 m
Ques. A ray of light travelling with a wavelength of 200 nm, Calculate its frequency? (2 marks)
Ans. Wavelength of light ray = 200 nm = 200 × 109 m
Speed of light ( c) = 3 × 108 m/sec
\(\text{Frequency} = \frac{\text{Speed of Light}}{\text{Wavelength}}\)
\(f = \frac{v}{\lambda}\)
= (3× 108 m/s)/ 200 × 109 m
= 1.5 × 1014 Hz
Ques. Find the wavelength of a wave traveling at 10 m/s at a frequency of 5 Hz? (2 marks)
Ans. As per the given question,
the Speed = 10 m/s
The Frequency = 5 Hz
Thus, by using the formula, we can obtain:
\(\lambda\) = c/f
= 10/5
= 2 m
Ques. Determine the wavelength of a wave which is travelling at the speed of 250 m/s with frequency of 600 Hz. (3 marks)
Ans. As per the question,
We can say, V = 250
f = 600
By using the formula,
V = \(\lambda\)f
Thus,
⇒ 250 = \(\lambda\) (600)
⇒ \(\lambda\) = 250/600
⇒ \(\lambda\) = 5/12
= 0.416 m
Ques. List the differences between Frequency and Wavelength. (5 marks)
Ans. The differences between Frequency and Wavelength are:
| Frequency | Wavelength |
|---|---|
| Frequency can be expressed as the number of complete wave cycles per second. | Wavelength can be expressed as the total distance covered to complete one wave. |
| Frequency helps to find Time. | Wavelength helps to find the Distance. |
| It is characterised by the symbol f. The SI unit of frequency is Hertz (Hz). | It is characterised by the symbol λ. The SI unit of Wavelength (λ) is meter (m). |
| Here, f = c/λ is the formula that helps to calculate frequency (c is the speed of light). | Here, λ = c/f is the formula that helps to calculate wavelength (c is the speed of light). |
| Frequency is used to find the recurrence of sound waves. | Wavelength is used to determine the length of sound waves. |
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