Definitions [2]
Definition: Free Vibration
The vibration that occurs without any external periodic force after an initial disturbance, where the body vibrates at its own natural frequency, is called free vibration.
Definition: Forced Vibration
The vibration that occurs due to a continuous external force acting on the system, where the body vibrates at the frequency of the external periodic force, is called forced vibration.
Theorems and Laws [2]
State law of linear density.
The fundamental frequency of vibrations of a string is inversely proportional to the square root of mass per unit length (linear density) if the tension and vibrating length of the string are constant.
∴ `n ∝ 1/sqrtm` ...(if T and l are constant.)
State law of length.
The fundamental frequency of vibrations of a string is inversely proportional to the length of the vibrating string if tension and mass per unit length are constant.
∴ n ∝ `1/l` ...(if T and m are constant.)
Key Points
Key Points: Free vs Forced Vibrations
| Sr. No. | Free Vibrations | Forced Vibrations |
|---|---|---|
| i. | Produced when a body is disturbed from its equilibrium position and released | Produced by an external periodic force of any frequency |
| ii. | Force is required initially only; then body vibrates on its own | Continuous external periodic force is required; if stopped, vibrations also stop |
| iii. | Frequency depends on the natural frequency of the body | Frequency depends on the frequency of the external periodic force |
| iv. | Energy remains constant in absence of friction/air resistance; decreases due to damping forces | Energy of the body is maintained constant by the external periodic force |
| v. | Amplitude decreases with time | Amplitude is small but remains constant as long as external periodic force acts |
| vi. | Vibrations stop sooner or later depending on the damping force | Vibrations stop as soon as the external periodic force is stopped |
Important Questions [39]
- A Sonometer Wire 1 Metre Long Weighing 2 G is in Resonance with a Tuning Fork of Frequency 300 Hz. Find Tension in the Sonometer Wire.
- Draw Neat, Labelled Diagrams for the Modes of Vibration of a Stretched String in Second Harmonic and Third Harmonic.
- A Stretched Sonometer Wire is in Unison with a Tuning Fork. When the Length of the Wire is Increased by 5%, the Number of Beats Heard per Second is 10. Find the Frequency of the Tuning Fork
- Show that all harmonics are present on a stretched string between two rigid supports.
- In the Stationary Wave, the Distance Between a Node and Its Adjacent Antinode is
- Show the Formation of Stationary Waves Diagramatically
- In Melde’S Experiment, When the Tension in the String is 10 G Wt Then Three Loops Are Obtained. Determine the Tension in the String Required to Obtain Four Loops, If All Other Conditions Are Constant.
- Hence Show that the Distance Between Node and Adjacent Antinode Is λ/4
- In Melde’S Experiment, the Number of Loops on a String Changes from 7 to 5 by the Addition of 0.015 Kgwt. Find the Initial Tension Applied to the String
- The fundamental frequency of transverse vibration of a stretched string of radius r is proportional to
- Explain Analytically How the Stationary Waves Are Formed
- Explain the Formation of Stationary Waves by Analytical Method. Show that Nodes and Antinodes Are Equally Spaced in Stationary Waves.
- Calculate the Ratio of Lengths of Their Air Columns
- In a set, 21 turning forks are arranged in a series of decreasing frequencies. Each tuning fork produces 4 beats per second with the preceding fork. If the first fork is an octave of the last fork, find the frequencies of the first and tenth fork.
- The Value of End Correction for an Open Organ Pipe of Radius 'R' is
- With a neat labelled diagram, show that all harmonics are present in an air column contained in a pipe open at both the ends. Define end correction.
- A pipe which is open at both ends is 47 cm long and has an inner diameter 5 cm. If the speed of sound in air is 348 m/s, calculate the fundamental frequency of air column in that pipe.
- A pipe open at both ends resonates to a frequency ‘n1’ and a pipe closed at one end resonates to a frequency ‘n2’. If they are joined to form a pipe closed at one end, then the fundamental frequency will be
- Two Sound Notes Have Wavelengths 83/170 M and 83/172 M in the Air. These Notes When Sounded Together Produce 8 Beats per Second. Calculate the Velocity of Sound in the Air And Frequencies of the Two Notes.
- Discuss Different Modes of Vibrations in an Air Column of a Pipe Open at Both the Ends.
- State the Cause of End Correction.
- Find the End Correction for the Pipe Open at Both the Ends In Fundamental Mode.
- A Tube Open at Both Ends Has Length 47 Em. Calculate the Fundamental Frequency of Air Column. (Neglect End Correction. Speed of Sound in Air is 3.3 X 102m/S
- Draw Neat Labelled Diagrams for Modes of Vibration of an Air Column in a Pipe When It Is Closed at One End.
- What is Meant by Hamonics?
- Show that Only Odd Harmonics Are Present as Overtones in the Case of an Air Column Vibrating in a Pipe Closed at One End.
- Show that Even as Well as Odd Harmonics Are Present as Overtones in the Case of an Air Column Vibrating in a Pipe Open at Both the Ends.
- A Wheel of Moment of Inertia 1 Kg.M2 is Rotating at a Speed of 30 Rad/S. Due to Friction on the Axis, It Comes to Rest in 10 Minutes. Calculate the Average Torque of the Friction.
- State law of linear density.
- Differentiate between free and forced vibrations.
- What Are Forced Vibrations and Resonance? Show that Only Odd Harmonics Are Present in an Air Column Vibrating in a Pipe Closed at One End.
- A Stretched Wire Emits a Fundamental Note of Frequency 256 Hz. Keeping the Stretching Force Constant and Reducing the Length of Wire by 10 Cm, the Frequency Becomes 320 Hz. Calculate the Original Length of Wire.
- A Sonometer Wire Vibrates with Three Nodes and Two Antinodes, the Corresponding Mode of Vibration is
- Distinguish Between Forced Vibrations and Resonance.
- State law of length.
- Show that Only Odd Harmonics Are Present in an Air Column Vibrating in a Pipe Closed at One End.
- Assuming Expression for Impedance in a Parallel Resonant Circuit, State the Conditions for Parallel Resonance. Define Resonant Frequency and Obtain an Expression for It.
- If Sound Waves Are Reflected from Surface of Denser Medium, There is Phase Change of
- What Should Be Tension Applied to a Wire of Length 1 M and Mass 10 Gram, If It Has to Vibrate with Fundamental Frequency of 50 Hz?
