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Chapter Elite-20 Challenge Zone

Target Advanced

LEVELJEE Advanced

A train approaching a hill at a speed of $40 km/h$ sounds a whistle of frequency $580 Hz$ when it is at a distance of $1 km$ from a hill. A wind with a speed of $40 km/h$ is blowing in the direction of motion of the train. Find (a) the frequency of the whistle as heard by an observer on the hill, (b) the distance from the hill at which the echo from the hill is heard by the driver and its frequency. (Velocity of sound in air = $1200 km/h$ )

JEE Advanced 2000

LEVELJEE Advanced

A 3.6 m long pipe resonates with a source of frequency 212.5 Hz when water level is at certain heights in the pipe. Find the heights of water level (from the bottom of the pipe) at which resonances occur. Neglect end correction. Now the pipe is filled to a height $H (\approx 3.6 m)$ . A small hole is drilled very close to its bottom and water is allowed to leak. Obtain an expression for the rate of fall of water level in the pipe as a function of $H$ . If the radii of the pipe and the hole are $2 \times 1 0^{- 2} m$ and $1 \times 1 0^{- 3} m$ respectively. Calculate the time interval between the occurrence of first two resonances. Speed of sound in air is $340 m/s$ and $g = 10 m/s^{2}$ .

JEE Advanced 2014

LEVELJEE Advanced

A student is performing an experiment using a resonance column and a tuning fork of frequency $244 s^{- 1}$ . He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $(0.350 \pm 0.005) m$ , the gas in the tube is: Useful information: * $167 R T = 640 J^{1/2} mole^{- 1/2}$ * $140 R T = 590 J^{1/2} mole^{- 1/2}$ The molar masses $M$ in grams are given in the options. Take the value of $10/ M$ for each gas as given there.

(A)

Neon (

M = 20, 10/ M = 7/10

)

(B)

Nitrogen (

M = 28, 10/ M = 3/5

)

(C)

Oxygen (

M = 32, 10/ M = 9/16

)

(D)

Argon (

M = 36, 10/ M = 17/32

)

JEE Advanced 2017

LEVELJEE Advanced

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 $λ_{0}$ is produced at point $O$ on the rope. The pulse takes time $T_{O A}$ to reach point $A$ . If the wave pulse of wavelength $λ_{0}$ is produced at point $A$ (Pulse 2) without disturbing the position of $M$ it takes time $T_{A O}$ to reach point $O$ . Which of the following options is/are correct?

* Multiple Correct Options

(A)

The time

T_{A O} = T_{O A}

(B)

The wavelength of Pulse 1 becomes longer when it reaches point

A

(C)

The velocity of any pulse along the rope is independent of its frequency and wavelength

(D)

The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the mid-point of rope

JEE Advanced 1994

LEVELJEE Advanced

A metallic rod of length $1 m$ is rigidly clamped at its mid-point. Longitudinal stationary waves are set-up in the rod in such a way that there are two nodes on either side of the mid-point. The amplitude of an antinode is $2 \times 1 0^{- 6} m$ . Write the equation of motion at a point $2 cm$ from the mid-point and those of the constituent waves in the rod. (Young's modulus of the material of the rod $= 2 \times 1 0^{11} Nm^{- 2}$ ; density $= 8000 kg m^{- 3}$ )

JEE Advanced 1991

LEVELJEE Advanced

The displacement of the medium in a sound wave is given by the equation $y_{i} = A cos (a x + b t)$ where $A$ , $a$ and $b$ are positive constants. The wave is reflected by an obstacle situated at $x = 0$ . The intensity of the reflected wave is $0.64$ times that of the incident wave. (a) What are the wavelength and frequency of incident wave? (b) Write the equation for the reflected wave. (c) In the resultant wave formed after reflection, find the maximum and minimum values of the particle speeds in the medium. (d) Express the resultant wave as a superposition of a standing wave and a travelling wave. What are the positions of the antinodes of the standing wave? What is the direction of propagation of travelling wave?

JEE Advanced 1990

LEVELJEE Advanced

A source of sound is moving along a circular path of radius $3 m$ with an angular velocity of $10 rad/s$ . A sound detector located far away from the source is executing linear simple harmonic motion along the line $B D$ with an amplitude $B C = C D = 6 m$ . The frequency of oscillation of the detector is $5/ π$ per second. The source is at the point $A$ when the detector is at the point $B$ . If the source emits a continuous sound wave of frequency $340 Hz$ , find the maximum and the minimum frequencies recorded by the detector. (Speed of sound = $340 m/s$ )

JEE Advanced 1993

LEVELJEE Advanced

Two radio stations broadcast their programmes at the same amplitude $A$ and at slightly different frequencies $ω_{1}$ and $ω_{2}$ respectively, where $ω_{1} - ω_{2} = 1 0^{3} Hz$ . A detector receives the signals from the two stations simultaneously. It can only detect signals of intensity $\geq 2 A^{2}$ . (a) Find the time interval between successive maxima of the intensity of the signal received by the detector. (b) Find the time for which the detector remains idle in each cycle of the intensity of the signal.

JEE Advanced 2001

LEVELJEE Advanced

A boat is travelling in a river with a speed $10 m/s$ along the stream flowing with a speed $2 m/s$ . From this boat a sound transmitter is lowered into the river through a rigid support. The wavelength of the sound emitted from the transmitter inside the water is $14.45 mm$ . Assume that attenuation of sound in water and air is negligible. (a) What will be the frequency detected by a receiver kept inside the river downstream? (b) The transmitter and the receiver are now pulled up into air. The air is blowing with a speed $5 m/s$ in the direction opposite to the river stream. Determine the frequency of the sound detected by the receiver. (Temperature of the air and water $= 2 0^{\circ} C$ ; Density of river water $= 1 0^{3} kg/m^{3}$ ; Bulk modulus of the water $= 2.088 \times 1 0^{9} Pa$ ; Gas constant $R = 8.31 J/mol-K$ ; Mean molecular mass of air $= 28.8 \times 1 0^{- 3} kg/mol$ ; $\frac{C _{p}}{C _{v}}$ for air $= 1.4$ )

JEE Advanced 1987

LEVELJEE Advanced

The following equations represent transverse waves: $z_{1} = A cos (k x - ω t)$ $z_{2} = A cos (k x + ω t)$ $z_{3} = A cos (k y - ω t)$ Identify the combination(s) of the waves which will produce: (a) standing wave(s), (b) a wave travelling in the direction making an angle of $4 5^{\circ}$ with the positive $X$ and positive $Y$ -axes. In each case, find the position at which the resultant intensity is always zero.

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

A train is moving at a constant speed of $v = 90 km/h$ on a straight level track. From a railway station P on the track, there is a village Q at a distance $y = 1.2 km$ in a direction perpendicular to the track. When the engine E is $x = 1.6 km$ away from the station, the driver honks a beep of horn of duration $τ = 44 s$ . Calculate durations of the honking $τ_{P}$ and $τ_{Q}$ heard at the station and in the village. Speed of sound in still air is $c = 350 m/s$ and there is no wind.

JEE Advanced 2023

LEVELJEE Advanced

Comprehension Passage

S_1 and S_2 are two identical sound sources of frequency

656 Hz

. The source S_1 is located at O and S_2 moves anti-clockwise with a uniform speed

42 ms^{- 1}

on a circular path around O, as shown in the figure. There are three points P, Q and R on this path such that P and R are diametrically opposite while Q is equidistant from them. A sound detector is placed at point P. The source S_1 can move along direction OP. [Given: The speed of sound in air is

324 ms^{- 1}

]

Question 1:

When only S_2 is emitting sound and it is Q, the frequency of sound measured by the detector in Hz is _____.

Question 2:

Consider both sources emitting sound. When S_2 is at R and S_1 approaches the detector with a speed $4 ms^{- 1}$ , the beat frequency measured by the detector is _______Hz.

JEE Advanced 2019

LEVELJEE Advanced

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is ______. [Speed of the sound = 330 m/s]

JEE Advanced 2024

LEVELJEE Advanced

Two uniform strings of mass per unit length $μ$ and $4 μ$ , and length $L$ and $2 L$ , respectively, are joined at point O, and tied at two fixed ends P and Q, as shown in the figure. The strings are under a uniform tension T. If we define the frequency $ν_{0} = \frac{1}{2 L} \frac{T}{μ}$ , which of the following statement(s) is(are) correct?

* Multiple Correct Options

(A)

With a node at O, the minimum frequency of vibration of the composite string is

ν_{0}

(B)

With an antinode at O, the minimum frequency of vibration of the composite string is

2 ν_{0}

(C)

When the composite string vibrates at the minimum frequency with a node at O, it has 6 nodes, including the end nodes.

(D)

No vibrational mode with an antinode at O is possible for the composite string.

JEE Advanced 2025

LEVELJEE Advanced

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 $θ_{0} = cos^{- 1} (0.9)$ 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 $g = 10 m/s^{2}$ ) is ___

JEE Main 2026

LEVELJEE Advanced

List-I shows four configurations made of straight and semi-circular narrow tubes containing air. A sound wave of wavelength $λ = 0.29 m$ enters these structures at the point $S$ and a sound detector is placed at $D$ . Between the points $S$ and $D$ , the sound travels only through the tubes. List-II contains the possible smallest values of $l$ (refer to the figures) for which the detector $D$ records maximum amplitude. Ignore effects of sharp corners. [Given $cos (1 5^{\circ}) = 0.97$ ]

List-I

List-II

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from $420 Hz$ to $490 Hz$ , when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is $330 ms^{- 1}$ .

(A)

81 kmh^{- 1}

(B)

91 kmh^{- 1}

(C)

71 kmh^{- 1}

(D)

61 kmh^{- 1}

JEE Main 2020

LEVELJEE Advanced

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears $2 beats/s$ . The oscillation frequency of each tuning fork is $ν_{0} = 1400 Hz$ and the velocity of sound in air is $350 m/s$ . The speed of each tuning fork is close to

(A)

\frac{1}{8} m/s

(B)

\frac{1}{2} m/s

(C)

1 m/s

(D)

\frac{1}{4} m/s

JEE Main 2019

LEVELJEE Advanced

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency $512 Hz$ produces first resonance when the tube is filled with water to a mark $11 cm$ below a reference mark near the open end of the tube. The experiment is repeated with another fork of frequency $256 Hz$ which produces first resonance when water reaches a mark $27 cm$ below the reference mark. The velocity of sound in air, obtained in the experiment is close to

(A)

328 ms^{- 1}

(B)

341 ms^{- 1}

(C)

322 ms^{- 1}

(D)

335 ms^{- 1}

JEE Main 2013

LEVELJEE Advanced

A sonometer wire of length $1.5 m$ is made of steel. The tension in it produces an elastic strain of $1%$ . What is the fundamental frequency of steel, if density and elasticity of steel are $7.7 \times 1 0^{3} kg/m^{3}$ and $2.2 \times 1 0^{11} N/m^{2}$ , respectively?

(A)

188.5 Hz

(B)

178.2 Hz

(C)

200.5 Hz

(D)

770 Hz

Micro-Topic Strategy Matrix

Wave Equation and Wave Speed

Reflection and Transmission of Waves

Standing Waves in Strings and Organ Pipes

Interference of Waves

Doppler Effect

Chapter Elite-20 Challenge Zone

Comprehension Passage

When only S_2 is emitting sound and it is Q, the frequency of sound measured by the detector in Hz is _____.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider both sources emitting sound. When S_2 is at R and S_1 approaches the detector with a speed 4 ms−1, the beat frequency measured by the detector is _______Hz.

List-I

List-II

Consider both sources emitting sound. When S_2 is at R and S_1 approaches the detector with a speed $4 ms^{- 1}$ , the beat frequency measured by the detector is _______Hz.