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The relation between Amplitude and Frequency can be depicted in the form of a sine waveform. Amplitude is the wave’s highest deviation from zero, while the frequency is the number of oscillations/waves that pass through a given point in a second.
- The relation between the amplitude and frequency cannot be depicted directly.
- It is depicted by rearranging the wave equation.
- Amplitude is inversely proportional to frequency.
- This means amplitude increases with a decrease in frequency.
- It also depends upon the oscillation of waves.
- The relation between amplitude and frequency is an important concept in periodic motion.
- When an individual is increasing the volume of TV, as a result, the amplitude of sound waves increases.
- In this case the frequency of sound waves decreases.
- The relationship can mathematically be represented as:
y(t) = Asin(2πft+Φ)
Key Terms: Relation between Amplitude and Frequency, Amplitude, Frequency, Wave, Time, Function, Periodic Motion, Sound Waves, Sine Waveform, Wavelength
Relationship Between Amplitude and Frequency
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The relationship between amplitude and frequency can be created in such a way that uniform motion will have a uniform angular velocity. Amplitude modulation is a type of function that consists of two time periods.
- The net force acting on the object depends on the direction of acceleration.
- Most common example of amplitude and frequency is the working of simple pendulum.
- The formula of the relation between amplitude and frequency in the sine waveform is given as:
A= ytsin(2πft+∅)
Where:
- A is the amplitude of the wave
- t is the time
- y(t) is the sine wave as a time function
- f is the frequency of the wave
- ∅ is the wave phase of the wave position when t=0.
Relationship Between Amplitude and Frequency
Waves Class 11 Notes PDF
Relationship between Amplitude and Frequency Formula
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The amplitude of a sound wave refers to the amount of displacement of vibrating particles of the medium from their actual position when the required sound is produced.
- It depends upon the loudness of the wave.
- Amplitude of the required wave is directly proportional to the loudness of the medium.
- Frequency of oscillations is defined as number of waves passing per second.
- The amplitude specifies maximum deviation from zero.
- It can be represented mathematically as:
Frequency = 1/Period
Amplitude and Frequency
Frequency to Amplitude Formula
We can figure out the formula of frequency to amplitude to calculate the frequency in the amplitude terms. For this, we need to rearrange the wave equation:
- The formula of frequency to amplitude is given as:
f= sin-1y(t)A-∅2πt
Amplitude to Frequency Formula
As we can calculate the frequency in terms of amplitude, the same way we can calculate the amplitude in terms of frequency. The formula for the amplitude to frequency formula is given as:
A= ytsin(2πft+∅)
Real-Life Example of Frequency and AmplitudeExample: Let us assume that person X is climbing the small mountains while the other person Y is climbing the large mountains. X climbed the mountains and completed the journey while Y was still busy climbing the mountains.
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Read More:
| Chapter Related Concepts | ||
|---|---|---|
| Loudness of Sound | Gravity Waves | LC Oscillation |
| Wave Power | Ground Wave propagation | Resonance |
Difference between Amplitude and Frequency
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The difference between amplitude and frequency are as follows:
| Amplitude | Frequency |
|---|---|
| Amplitude is the highest deviation of a wave from the initial point which is zero. | Frequency is the total number of waves per second that passes through a given point. |
| It s measured in meters. | It is measured in Hertz. |
| Amplitude is used to calculate the size of waves. | Frequency is used to calculate the number of waves. |
Things to Remember
- The relationship between amplitude and frequency is in the form of the sine wave.
- Frequency is the number of times any event repeats at a specific time.
- The SI unit of frequency is Hertz.
- Amplitude is the highest wave deviation from an initial point such as zero.
- It is used in the medical fields and the domains where the oscillatory and vibratory phenomena are used.
- The formula of the relation between frequency and amplitude is given as A= ytsin(2πft+∅).
- The formula to calculate the amplitude in terms of frequency is the same as that of the relation between them.
Read More:
| Class 11 Physics Related Concept | ||
|---|---|---|
| Interference of Waves | ||
| Waves Important Questions | ||
Sample Questions
Ques. Write the formula to show the relationship between the frequency and the amplitude. (3 marks)
Ans. The formula to show the relationship between amplitude and frequency in the form of the sine wave function is
A= ytsin(2πft+∅)
Where:
- A is the amplitude of the wave
- t is the time
- y(t) is the sine wave as a time function
- f is the frequency of the wave
- ∅ is the wave phase of the wave position when t=0.
Ques. Explain the form in which the amplitude is measured in the case of a longitudinal wave. (2 marks)
Ans. In the case of a longitudinal wave or a sound wave, we measure the amplitude in form of a particle’s maximum displacement from its point of equilibrium. When the amplitude of a wave loses its energy, it reduces at a slow pace.
Ques. Define amplitude with an example. (2 marks)
Ans. Amplitude is defined as an object in the periodic motion that depicts the maximum displacement from the point of equilibrium. An example of amplitude can be a pendulum that swings back and forth to the maximum distance from the point of equilibrium.
Ques. Can we say that the amplitude is dependent on frequency? (2 marks)
Ans. No, the amplitude is not dependent on the frequency rather it is dependent on the total energy possessed by a system. In general terms, the amplitude of any system can vary but the frequency remains unchanged.
- An example can be two persons climbing the stairs.
- However, the number of stairs remains the same but it depends on the energy of both the persons if they could make it to the destination or not.
Ques. Define frequency and mention its application. (3 marks)
Ans. Frequency is the number of times any event repeats at a specific time. It is measured in Hertz. It simply means how frequent an event is.
- It is applied in the oscillatory and vibratory phenomena where one can calculate the audio signals, light, mechanical vibrations, radio waves, or in the medical science to keep track of a person’s heartbeat.
Ques. Can we calculate the frequency in terms of amplitude? If yes, then state the formula through which one can do so. (2 marks)
Ans. Yes, we can measure the frequency in terms of amplitude. To achieve its formula, we have to rearrange certain terms in the wave formula. The resultant formula of measuring the frequency in terms of amplitude is:
f= sin-1y(t)A-∅2πt
Ques. State the two differences between the amplitude and the frequency. (3 marks)
Ans. Two differences are:
- Amplitude is defined as an object in the periodic motion that depicts the maximum displacement from the point of equilibrium while frequency is the number of times any event repeats at a specific time.
- Amplitude is required to measure the size of the waves while frequency is required to calculate the total number of waves in a given system.
- The unit of amplitude is metres and the unit of frequency is Hertz (Hz).
Ques. Determine the wavelength of a wave travelling at 500 m/s at a frequency of 11 Hz. (2 marks)
Ans. By using the formula,
λ=c/f
Thus,
= 500/11
= 45.45 m
Ques. Determine the wavelength of a wave which is travelling at the speed of 150 m/s with frequency of 500 Hz. (3 marks)
Ans. As per the question,
We can say, V = 150
f = 500
By using the formula,
V = λf
Thus,
⇒ 150 = λ(500)
⇒ λ = 150/500
⇒ λ= 3/10
= 0.30 m
Ques. A fork vibrates with a frequency of 250. If the velocity of sound is 340.6 m/s. Find the wavelength and distance, which the sound travels during the time the fork makes 50 vibrations. (3 Marks)
Ans. According to the question,
- Frequency f = 250
- Wave Velocity V = 340.6 m/s
- Wavelength λ =?
Using the Relation between Velocity and Frequency, we get
V=f×λ
λ = V/f
λ = 340.6/250 = 1.35m
Thus, the wavelength is 1.36 m.
The distance traveled in 50 vibrations = 50 × 1.36 = 68.12m
Ques. From a radio station, the frequency of radio waves is 18 megacycles/sec. Calculate the wavelength. (3 Marks)
Ans. It is given that,
Frequency f = 18 megacycle/sec = 18 x106 cycles/sec
Since the velocity of radio waves is equal to the velocity of light in a vacuum, thus,
V = 3 × 108m/s
λ =V/f
λ = (3 × 108m/s)/(18 x106) = 16.67m
Thus, the wavelength of the radio wave is 16.67 m.
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