{"id":5394,"date":"2021-12-21T13:18:11","date_gmt":"2021-12-21T07:48:11","guid":{"rendered":"https:\/\/acejee.com\/blog\/?p=5394"},"modified":"2024-09-30T08:10:12","modified_gmt":"2024-09-30T02:40:12","slug":"waves-dpp-jee-main-jee-advanced","status":"publish","type":"post","link":"https:\/\/acejee.com\/blog\/waves-dpp-jee-main-jee-advanced\/","title":{"rendered":"Waves | DPP | JEE Main | JEE Advanced"},"content":{"rendered":"\t\t
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Q1 A string of length $L$ and mass $M$ hangs freely from a fixed point. Calculate the velocity of the transverse wave travelling along the string, at a point which is at a distance $x$ from the bottom of the string.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$v = \\sqrt{gx}$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q2 A source of sound of frequency $256 \\ Hz$ is moving rapidly towards a wall with a velocity of $5 \\ m\/s$. How many beats per second will be heard if sound travels at a speed of $330 \\ m\/s$ and the source is between the wall and the observer?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$8$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q3 Standing waves are produced by the superposition of two waves:<\/p>

$y_1 = 0.05 \\sin (3 \\pi t – 0.5 \\pi x)$ and $y_2 = 0.05 \\sin (3 \\pi t + 0.5 \\pi x)$, where $x$ and $y$ are measured in meter and $t$ in second. Find the amplitude of the particle located at $x = 0.5 \\ m$.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$\\cfrac{01}{\\sqrt{2}} \\ m$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q4 A standing wave set up in a medium is given by $y = 4 \\cos \\left(\\cfrac{\\pi x}{3}\\right) \\sin 40 \\pi t$ where $x$ and $y$ are in $cm$ and $t$ is in seconds,<\/p>

(a) What are the amplitude and velocity of the two component waves which produce this standing wave?<\/p>

(b) What is the distance between the adjacent nodes?<\/p>

(c) What is the velocity of the particle of the medium at $x = 3 \\ cm$ at time $t = \\cfrac{1}{8} \\ sec$?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(a) $2 \\ cm, \\ 120 \\ m\/s$<\/p>

(b) $3 \\ cm$<\/p>

(c) $160 \\pi \\ cm\/sec$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q5 A $2 \\ m$ long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is $200 \\ m\/s$ and the amplitude of standing wave is $0.5 \\ cm$.<\/p>

(a) Find the wavelength and the frequency<\/p>

(b) Write the equation giving the displacement of different points as a function of time. Choose the $X$-axis along the string with the origin at one end and $t = 0$ at the instant when the point $x = 50 \\ cm$ reached its maximum displacement.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(a) $2 \\ m, \\ 100 \\ Hz$;<\/p>

(b) $(0.5 \\ cm)$ $\\sin$$ [(\\pi m^{-1})x]$ $\\cos$$ [(200 \\ \\pi s^{-1})t]$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q6 A bus is moving towards a huge wall with a velocity of $5 \\ m\/s$. The driver sounds a horn of frequency $200 \\ Hz$. The frequency of the beats heard by a passenger of the bus will be (in $Hz$) nearly ( velocity of sound in air $ = 338 \\ m\/s$)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$6$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q7 A string is stretched along the $X$ axis. A disturbance given by the equation $y(x, t) = 4 \\sin \\left(\\cfrac{\\pi x}{3}\\right) \\cos (10 \\pi t)$, is produced in the string. Where $X$ is in $cm$ and $t$ is in seconds. If the Distance between two adjacent nodes is $n \\ cm$, then find the value of $n$.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$3$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q8 When two progressive waves $y_1 = 4 \\sin (2x – 6 t)$ and $y_2 = 4 \\sin \\left(2x – 6t – \\cfrac{2 \\pi}{3}\\right)$ are superimposed, find the amplitude of the resultant wave.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$4$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q9 The fundamental frequency of a sonometer wire increases by $6 \\ Hz$ if its tension is increased by $44$% keeping the length constant. What will be the change in the fundamental frequency when length of wire is increased by $20$% keeping the original tension in the wire.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$5$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q10 An open pipe is suddenly closed at one end, as a result of which the frequency of third harmonic of the closed pipe is found to be $100 \\ Hz$ higher than the fundamental frequency of the open pipe. If fundamental frequency of the open pipe is $400\/n \\ Hz$. Find the value of $n$.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$2$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q11 A simple harmonic wave has the equation $y = 0.5 \\sin (314 t – 1.57 x)$, where $y, \\ x$ are in meters and $t$ is in seconds.<\/p>

(a) Find the frequency and the wavelength of this wave.<\/p>

(b) Another wave has the equation $y’ = 0.1 \\sin (314 t – 1.57 x + 1.57)$. Deduce the Phase difference between them and the ratio of their intensities.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(a) $50 \\ Hz, \\ 4 \\ m$<\/p>

(b) $\\pi\/2, \\ 25$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q12 The water level in a vertical glass tube $1 \\ m$ long can be adjusted to any position in the tube. A tuning fork vibrating at $686 \\ Hz$ is held just over the open top end of the tube. At what positions the water level will there be resonance? ( velocity of sound $ = 330 \\ m\/s$)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$12 \\ cm, \\ 36 \\ cm, \\ 60 \\ cm, \\ 84 \\ cm$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q13 A tuning fork $P$ of unknown frequency gives $7$ beats in $2$ second with another tuning fork $Q$. When $Q$ is moved rightward towards a wall with speed $5 \\ m\/s$, it gives $5$ beats per Second for a stationary observer located left to it. On filing, $P$ gives $6$ beats per second with $Q$. What is the frequency of $P$? [Speed of sound $ = 332 \\ m\/s$].<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$169.5 \\ Hz$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q14 A steel wire is rigidly fixed at both ends. Its length, mass and cross-sectional area are $1 \\ m, \\ 0.1 \\ kg$ and $10^{-8} \\ m^2$ respectively. Tension in the wire is produced by lowering the temperature by $20^{\\circ}C$. If transverse waves are set up by plucking the wire at $0.25 \\ m$ from one end, and assuming that the wire vibrates with minimum number of loops possible for such a case. The frequency of vibration (in $Hz$) is found to be $11K$. Find the value of $K$. Given $\\alpha = 1.21 \\times 10^{-5} \\ {^{\\circ}C^{-1}}, \\ Y = 2 \\times 10^{11} \\ N\/m^2$.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$2$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q15 A point like sound source emits sound in all direction uniformly. An observer who is at a distance of $50 \\ m$ from the source detects sound of intensity $10^{-5} \\ watt\/m^2$. If the bulk modulus of air is $1.6 \\times 10^5 \\ N\/m^2$ and velocity of sound is $340 \\ m\/a$. Find power developed by sound source and pressure amplitude at the position of observer.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$3.14 \\times 10^{-4} \\ Watt, \\ 3.07 \\times 10%{-3} \\ N\/m^2$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q16 Acceleration of point $x = 2 \\ m$ of a transverse wave is $5 \\hat{j} \\ m\/s^2$ and the slope of waveform is given by $\\cfrac{dy}{dx} = 5 \\sin \\cfrac{\\pi}{12}x$. Then the speed of the point at that instant is given in $m\/s$ as<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$\\sqrt{\\cfrac{150}{\\pi \\sqrt{3}}}$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q17 The speed of sound in air is $332 \\ m\/s$ at NTP. What will be the speed of sound in hydrogen at NTP if the density of hydrogen at NTP is $1\/16$ that of air $[$assume $P_H = P_{\\text{air}}]$?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$1328 \\ m\/s$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q18 Two wires made up of same material and having same length and radii $r$ and $2r$, respectively, are welded together end to end. This combination is used as a sonometer wire, kept under tension $T$. The welded point is midway between the two bridges. What would be the ratio of the number of loops formed in the wires such that the joint is a node when stationary vibrations are set up in the wires.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$n_r : n_{2r} = 1 : 2$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q19 Two tuning forks $A$ and $B$ give three beats per second. A resonates with a closed column of air $30 \\ cm$ long and $B$ with an open column $71 \\ cm$ long, both in their fundamental modes. Calculate the frequencies of the tuning forks.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$19.32 \\ Hz, \\ 16.32 \\ Hz$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q20 A transverse wave is travelling along a string from left to right. Adjoining figure represents the snapshot at a given instant. At this instant,<\/p>

(a) which of the points will have an upward velocity?<\/p>

(b) which of the points will have downward velocity?<\/p>

(c) which of the points have zero velocity?<\/p>

(d) which of the points have maximum magnitude of velocity ?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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(a) $D, E, F$;<\/p>

(b) $A, B, H, I$;<\/p>

(c) $C, G$;<\/p>

(d) $A, E, I$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q21 A person standing between two parallel hills fires a gun. He hears the first echo after $1.5 \\ sec$ and the second after $2.5 \\ sec$. If the speed of sound in air is $332 \\ m\/s$. Then find the time (in $sec$) when he hear the third echo?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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$4$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q22 Two identical flutes produces fundamental notes of frequency $300 \\ Hz$ at $27^{\\circ}C$. If the temperature of the air in one flute is increased to $31^{\\circ}C$. Find the number of beats (approx.) heard per second.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/i><\/span>\n\t\t\t\t\t\t\t\t<\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\tAnswer<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t

$2$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q23 A tuning fork produces first resonance in a glass tube containing an air column when the length of the air column was $44 \\ cm$ and again when length was $140 \\ cm$ in the same tube. Calculate the end correction in $cm$.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/i><\/span>\n\t\t\t\t\t\t\t\t<\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\tAnswer<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t

$4$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Q24 A closed organ pipe and an open pipe of the same length produce $4$ beats when they are set into vibrations simultaneously. If the length of each of them were twice their initial lengths, then find the number of beats produced. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/i><\/span>\n\t\t\t\t\t\t\t\t<\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\tAnswer<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t

$2$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

Practice problems for transverse and longitudinal waves which will help you enhance your problem solving skills for JEE Main and JEE Advanced<\/p>\n","protected":false},"author":1,"featured_media":5471,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"0","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"on","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"off","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","cybocfi_hide_featured_image":"yes","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"off","ocean_gallery_id":[],"footnotes":""},"categories":[17],"tags":[],"class_list":["post-5394","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-jee-physics-questions","entry","has-media"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/posts\/5394","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/comments?post=5394"}],"version-history":[{"count":1,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/posts\/5394\/revisions"}],"predecessor-version":[{"id":9430,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/posts\/5394\/revisions\/9430"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/media\/5471"}],"wp:attachment":[{"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/media?parent=5394"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/categories?post=5394"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/acejee.com\/blog\/wp-json\/wp\/v2\/tags?post=5394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}