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?

u = 0 . 5 v and f s = 1 . 5 f 0

u = 0 . 8 v and f s = 0 . 5 f 0

In an experiment, to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50 .7 cm and 83 .9 cm . Which of the following statements is (are) true?

The wavelength of the sound wave is 66 .4 cm .

The resonance at 50 .7 cm corresponds to the fundamental harmonic.

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JEE Advanced

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Two vectors $\vec{A}$ and $\vec{B}$ are defined as $\vec{A} = a \hat{i}$ and $\vec{B} = a (\cos ω t \hat{i} + \sin ω t \hat{j})$ , where a is a constant and $ω = \frac{π}{6} rad s^{- 1} .$ If $|\vec{A} + \vec{B}| = \sqrt{3} |\vec{A} - \vec{B}|$ at time $t = τ$ for the first time, the value of $τ$ in seconds, is_______

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Important Questions on Mechanical Wave

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Mechanical Wave>JEE Advanced Paper 1 - 2018>Q 9

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed

1 .0 m s^{- 1}

and the man behind walks at a speed

2 .0 m s^{- 1}

. A third man is standing at a height

12 m

above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency

1430 Hz

. The speed of sound in air is

330 m s^{- 1}

. At the instant, when the moving men are

10 m

apart, the stationary man is equidistant from them. The frequency of beats in

Hz

, heard by the stationary man at this instant, is __________.

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Mechanical Wave>JEE Advanced Paper 1 - 2017>Q 10

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_{O A}

to reach point O. Which of the following options is/are correct?
Question Image

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JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Mechanical Wave>JEE Advanced Paper 1 - 2016>Q 12

Two loudspeakers

M

and

N

are located

20 m

apart and emit sound at frequencies

118 Hz

and

121 Hz

, respectively. A car is initially at a point

P

1800 m

away from the midpoint

Q

of the line

M N

and moves towards

Q

constantly at

60 km h^{- 1}

along the perpendicular bisector of

M N

. It crosses

Q

and eventually reaches a point

R

1800 m

away from

Q

. Let

ν (t)

represent the beat frequency measured by a person sitting in the car at time

t

. Let

ν_{p}, ν_{Q} and ν_{R}

be the beat frequencies measured at locations

P, Q

and

R

, respectively. The speed of sound in air is

330 m s^{- 1} .

Which of the following statement(s) is (are) true regarding the sound heard by the person?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Mechanical Wave>JEE Advanced Paper 1 - 2014>Q 13

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:

\sqrt{167 R T} = 640 J^{\frac{1}{2}} m o l^{- \frac{1}{2}}; \sqrt{140 R T} = 590 J^{\frac{1}{2}} m o l^{- \frac{1}{2}}

. The molar masses

M

in grams are given in the options. Take the values of

\sqrt{\frac{10}{M}}

for each gas as given there.)

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Mechanical Wave>JEE Advanced Paper 1 - 2014>Q 14

One end of a taut string of length 3m along the x axis is fixed at x = 0. The speed of the waves in the string is

100 m s^{- 1}

. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

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JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 9 - Mechanical Wave>JEE Advanced Paper 1 - 2013>Q 15

A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation,

y (x, t) = (0 .01 m) sin [(62.8 m^{-1}) x] cos [(628 s^{-1}) t]

. Assuming

π = 3.14

, the correct statement(s) is (are):

Two vectors A→ and B→ are defined as A→=ai^ and B→=acosωti^+sinωtj^, where a is a constant and ω=π6 rad s-1. If A→+B→=3A→-B→ at time t=τ for the first time, the value of τ in seconds, is_______

Important Questions on Mechanical Wave

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