A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12} / \sec$. What is the force constant of the bonds connecting one atom with the other ? ( Mole wt. of silver $= 108 $ and Avogadro number $= 6.02 \times 10^{23} \, gm \, mole^{-1} $ )
- 6.4 N/m
- 7.1 N/m
- 2.2 N/m
- 5.5 N/m
The Correct Option is B
Solution and Explanation
$K x=m a $
$\Rightarrow a=( K / m ) x$
$T=2 \pi \sqrt{\frac{m}{K}}$
$f=\frac{1}{T}=\frac{1}{2 \pi} \sqrt{\frac{K}{m}}=10^{12}$
$=\frac{1}{4 \pi^{2}} \times \frac{K}{m}=10^{24}$
$K=4 \pi^{2} m \times 10^{24}=\frac{4 \times 10 \times 108 \times 10^{-3}}{6.02 \times 10^{23}} \times 10^{24}$
$=7.1 \,N / m$
Top Questions on Waves and Oscillations
- A simple pendulum has a length of $ L = 2 \, \text{m} $. What is the time period of the pendulum? (Assume $ g = 9.8 \, \text{m/s}^2 $)
- MHT CET - 2025
- Physics
- Waves and Oscillations
- Two tuning forks produce 6 beats per second when sounded together. One of the fork is in unison with 1.5 m length of wire and the other with 2.0 m length of wire. The frequencies of forks are:
- CUET (PG) - 2025
- Geophysics
- Waves and Oscillations
- A wave of frequency 500 Hz is travelling with a velocity 1000 m/s. How far are two points situated in wave whose displacement differ in phase by \( \frac{\pi}{3} \)?
- CUET (PG) - 2025
- Geophysics
- Waves and Oscillations
- A damped harmonic oscillator has an amplitude that reduces to half in 10 seconds. What will be the amplitude after 30 seconds?
- BITSAT - 2025
- Physics
- Waves and Oscillations
- Identify which of the following wave functions describe(s) travelling wave(s).
(\(A_0, B_0, a\), and \(b\) are positive constants of appropriate dimensions)- IIT JAM PHY - 2025
- Physics
- Waves and Oscillations
Questions Asked in JEE Main exam
- In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
- JEE Main - 2025
- Permutations
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):
- JEE Main - 2025
- Fluid Mechanics
- Let \( f: \mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \left( 2 + 3a \right)x^2 + \left( \frac{a+2}{a-1} \right)x + b, a \neq 1 \). If \[ f(x + y) = f(x) + f(y) + 1 - \frac{2}{7}xy, \] then the value of \( 28 \sum_{i=1}^5 f(i) \) is:
- JEE Main - 2025
- Functions
Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is:
- JEE Main - 2025
- Differential Calculus
- A 400 g solid cube having an edge of length \(10\) cm floats in water. How much volume of the cube is outside the water? (Given: density of water = \(1000 { kg/m}^3\))
Concepts Used:
Oscillations
Oscillation is a process of repeating variations of any quantity or measure from its equilibrium value in time . Another definition of oscillation is a periodic variation of a matter between two values or about its central value.
The term vibration is used to describe the mechanical oscillations of an object. However, oscillations also occur in dynamic systems or more accurately in every field of science. Even our heartbeats also creates oscillations. Meanwhile, objects that move to and fro from its equilibrium position are known as oscillators.
Read More: Simple Harmonic Motion
Oscillation- Examples
The tides in the sea and the movement of a simple pendulum of the clock are some of the most common examples of oscillations. Some of examples of oscillations are vibrations caused by the guitar strings or the other instruments having strings are also and etc. The movements caused by oscillations are known as oscillating movements. For example, oscillating movements in a sine wave or a spring when it moves up and down.
The maximum distance covered while taking oscillations is known as the amplitude. The time taken to complete one cycle is known as the time period of the oscillation. The number of oscillating cycles completed in one second is referred to as the frequency which is the reciprocal of the time period.