A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2\, m s^{-1}$ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is $320\, ms ^{-1}$, the smallest value of the percentage change required in the length of the pipe is ______.
Correct Answer: 0.62
Solution and Explanation
\(\text{The smallest value of the percentage change required in the length of the pipe is }\) \(\underline{0.62}.\)
Top Questions on Waves
- Two ropes of the same material of radius $ R $ and $ \frac{R}{2} $, what will be the ratio of wave speed in the second rope to the first? (They both are with the same tension)
- The amplitude and phase of the wave when two travelling waves given as $ y_1(x, t) = 4 \sin(\omega t - kx) $ and $ y_2(x, t) = 2 \sin\left(\omega t - kx + \frac{2\pi}{3}\right) $ are superimposed.
- How much time does a particle at \( x = C \) take to go from the mean position to the extreme (maximum displacement) for the first time?
- A particle on a string undergoes a transverse wave motion given by: \[ y = 5 \sin \left( 4 \pi t - \frac{\pi x}{2} \right) \] (All quantities in SI units.) How much time does a particle at \( x = 0 \) take to go from mean position to extreme (maximum displacement) for the first time?
Two plane polarized light waves combine at a certain point, whose "E" components are: \[ E_1 = E_0 \sin \omega t, \quad E_2 = E_0 \sin \left( \omega t + \frac{\pi}{3} \right) \] Find the amplitude of the resultant wave.
Questions Asked in JEE Advanced exam
A positive, singly ionized atom of mass number $ A_M $ is accelerated from rest by the voltage $ 192 \, \text{V} $. Thereafter, it enters a rectangular region of width $ w $ with magnetic field $ \vec{B}_0 = 0.1\hat{k} \, \text{T} $. The ion finally hits a detector at the distance $ x $ below its starting trajectory. Which of the following option(s) is(are) correct?
$ \text{(Given: Mass of neutron/proton = } \frac{5}{3} \times 10^{-27} \, \text{kg, charge of the electron = } 1.6 \times 10^{-19} \, \text{C).} $
- JEE Advanced - 2024
- Electromagnetic Field (EMF)
- Let \(\overrightarrow{OP}=\frac{\alpha-1}{\alpha}\hat{i}+\hat{j}+\hat{k},\overrightarrow{OQ}=\hat{i}+\frac{\beta-1}{\beta}\hat{j}+\hat{k}\) and \(\overrightarrow{OR}=\hat{i}+\hat{j}+\frac{1}{2}\hat{k}\) be three vector where α, β ∈ R - {0} and 0 denotes the origin. If \((\overrightarrow{OP}\times\overrightarrow{OQ}).\overrightarrow{OR}=0\) and the point (α, β, 2) lies on the plane 3x + 3y - z + l = 0, then the value of l is _______.
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- Vector Algebra
- Let \(S=\left\{(x,y)\in\R\times\R:x\ge0,y\ge0,y^2\le12-2x\ \text{and}\ 3y+\sqrt8\ x\le5\sqrt8\right\}\). If the area of the region S is \(\alpha\sqrt2\), then α is equal to
- JEE Advanced - 2024
- Coordinate Geometry
- Let \(S=\left\{\begin{pmatrix} 0 & 1 & c \\ 1 & a & d\\ 1 & b & e \end{pmatrix}:a,b,c,d,e\in\left\{0,1\right\}\ \text{and} |A|\in \left\{-1,1\right\}\right\}\), where |A| denotes the determinant of A. Then the number of elements in S is _______.
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- Matrices
- A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass \( m \) and radius \( r \) and is in a uniform vertical magnetic field \( B_0 \). When a current \( I \) is passed through the loop, the loop turns about the line PQ by an angle \( \theta \). The angle \( \theta \) is given by:
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- Electromagnetic Field (EMF)
Concepts Used:
Waves
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
- Water waves (ripples of gravity waves, not sound through water)
- Light waves
- S-wave earthquake waves
- Stringed instruments
- Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
Examples of longitudinal waves:
- Sound waves
- P-type earthquake waves
- Compression wave