A wave is represented by the equation ;
$\, \, \, \, \, y=A \sin (10 \pi x+15 \pi l+ \pi /3) $
where, x is in metre and t is in second. The expression represents
- a wave travelling in the positive x-direction with a velocity 1.5 m/s
- a wave travelling in the negative x-direction with a velocity 1.5 m/s
- a wave travelling in the negative x-direction with a wavelength 0.2 m
- a wave travelling in the positive x-direction with a wavelength 0.2 m
The Correct Option is C
Solution and Explanation
Speed of wave, $\, \, \, \, \, v=\frac {\omega}{k}=1.5 \, m/s $
Wavelength of wave $?= \frac {2 \pi }{k}= \frac {2 \pi }{10 \pi }=0.2 \, m $
$10 \pi x$ and $15 \pi t$ have the same sign. Therefore, wave is travelling in negative x-direction.
$\therefore $ Correct options are (b) and (c)
Top JEE Advanced Physics Questions
- A projectile of mass 200 g is launched in a viscous medium at an angle $60^\circ$ with the horizontal, with an initial velocity of 270 m/s. It experiences a viscous drag force $\vec{F} = -c \vec{v}$ where the drag coefficient $c = 0.1 \, \text{kg/s}$ and $\vec{v}$ is the instantaneous velocity of the projectile. The projectile hits a vertical wall after 2 s. Taking $e = 2.7$, the horizontal distance of the wall from the point of projection (in m) is ____
- JEE Advanced - 2025
- Physics
- Projectile motion
- Consider a star of mass $ m_2 $ kg revolving in a circular orbit around another star of mass $ m_1 $ kg with $ m_1 \gg m_2 $. The heavier star slowly acquires mass from the lighter star at a constant rate of $ \gamma $ kg/s. In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is $ r $, then its relative rate of change $ \frac{1}{r} \frac{dr}{dt} $ (in s$^{-1}$) is given by:
- JEE Advanced - 2025
- Physics
- Gravitation
- An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the $X$ axis. They are pulled from the equilibrium position in opposite directions along the $X$ axis by a small angular amplitude $\theta_0 = \cos^{-1}(0.9)$ and released simultaneously. If the natural frequency of the transmitter is 660 Hz and the speed of sound in air is 330 m/s, the maximum variation in the frequency (in Hz) as measured by the receiver (Take the acceleration due to gravity $g = 10\, \text{m/s}^2$) is ___
- JEE Advanced - 2025
- Physics
- Waves and Oscillations
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
- JEE Advanced - 2025
- Physics
- Dimensional Analysis
An ideal monatomic gas of $ n $ moles is taken through a cycle $ WXYZW $ consisting of consecutive adiabatic and isobaric quasi-static processes, as shown in the schematic $ V-T $ diagram. The volume of the gas at $ W, X $ and $ Y $ points are, $ 64 \, \text{cm}^3 $, $ 125 \, \text{cm}^3 $ and $ 250 \, \text{cm}^3 $, respectively. If the absolute temperature of the gas $ T_W $ at the point $ W $ is such that $ n R T_W = 1 \, J $ ($ R $ is the universal gas constant), then the amount of heat absorbed (in J) by the gas along the path $ XY $ is
- JEE Advanced - 2025
- Physics
- Thermodynamics
Top JEE Advanced Waves Questions
Consider a system of three connected strings, $ S_1, S_2 $ and $ S_3 $ with uniform linear mass densities $ \mu \, \text{kg/m}, 4\mu \, \text{kg/m} $ and $ 16\mu \, \text{kg/m} $, respectively, as shown in the figure. $ S_1 $ and $ S_2 $ are connected at point $ P $, whereas $ S_2 $ and $ S_3 $ are connected at the point $ Q $, and the other end of $ S_3 $ is connected to a wall. A wave generator $ O $ is connected to the free end of $ S_1 $. The wave from the generator is represented by $ y = y_0 \cos(\omega t - kx) $ cm, where $ y_0, \omega $ and $ k $ are constants of appropriate dimensions. Which of the following statements is/are correct:
- A source, approaching with speed $u$ towards the open end of a stationary pipe of length $L$, is emitting a sound of frequency $f _{ s }$. The farther end of the pipe is closed .The speed of sound in air is $v$ and $f _{0}$ is the fundamental frequency of the pipe. For which of the following combination(s) of $u$ and $f_{s}$, will the sound reaching the pipe lead to a resonance?
- A source, approaching with speed $u$ towards the open end of a stationary pipe of length $L$, is emitting a sound of frequency $f _{ s }$. The farther end of the pipe is closed .The speed of sound in air is $v$ and $f _{0}$ is the fundamental frequency of the pipe. For which of the following combination(s) of $u$ and $f_{s}$, will the sound reaching the pipe lead to a resonance?
- 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 ______.
- A block $M$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at $O$. A transverse wave pulse (Pulse 1) of wavelength $\lambda_{0}$ is produced at point $O$ on the rope. The pulse takes time $T_{OA}$ to reach point $A$. If the wave pulse of wavelength $\lambda_{0}$ is produced at point $A$ (Pulse 2) without disturbing the position of $M$ it takes time $T_{AO}$ to reach point $O$. Which of the following options is/are correct?
Top JEE Advanced Questions
- Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from 10 mg g$^{-1}$ and 16 mg g$^{-1}$ aqueous phenol solutions, the concentrations of adsorbed phenol are measured to be 4 mg g$^{-1}$ and 10 mg g$^{-1}$, respectively. At this temperature, the concentration (in mg g$^{-1}$) of adsorbed phenol from 20 mg g$^{-1}$ aqueous solution of phenol will be ____. Use: $\log_{10} 2 = 0.3$
- JEE Advanced - 2025
- Adsorption
Monocyclic compounds $ P, Q, R $ and $ S $ are the major products formed in the reaction sequences given below.
The product having the highest number of unsaturated carbon atom(s) is:
- JEE Advanced - 2025
- Organic Chemistry
For the reaction sequence given below, the correct statement(s) is(are):
- A linear octasaccharide (molar mass = 1024 g mol$^{-1}$) on complete hydrolysis produces three monosaccharides: ribose, 2-deoxyribose and glucose. The amount of 2-deoxyribose formed is 58.26 % (w/w) of the total amount of the monosaccharides produced in the hydrolyzed products. The number of ribose unit(s) present in one molecule of octasaccharide is _____.
Use: Molar mass (in g mol$^{-1}$): ribose = 150, 2-deoxyribose = 134, glucose = 180; Atomic mass (in amu): H = 1, O = 16- JEE Advanced - 2025
- Biomolecules
Consider a reaction $ A + R \rightarrow Product $. The rate of this reaction is measured to be $ k[A][R] $. At the start of the reaction, the concentration of $ R $, $[R]_0$, is 10-times the concentration of $ A $, $[A]_0$. The reaction can be considered to be a pseudo first order reaction with assumption that $ k[R] = k' $ is constant. Due to this assumption, the relative error (in %) in the rate when this reaction is 40% complete, is ____. [$k$ and $k'$ represent corresponding rate constants]
- JEE Advanced - 2025
- Chemical Kinetics
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