Waves - Mind Map based Questions

Which one of the following does not represent a traveling wave :
1. $y = \sin (x - v t)$
2. $y = y_{m} \sin k (x + v t)$
3. $y = y_{m} \sin (x - v t)$
4. $y = f (x^{2} - v t^{2})$

A transverse wave is represented by the equation $y = y_{0} \sin \frac{2 π}{λ} (v t - x)$
For what value of λ, the maximum particle velocity equal to two times the wave velocity?
(1) $λ = 2 π y_{0}$
(2) $λ = π y_{0} / 3$
(3) $λ = π y_{0} / 2$
(4) $λ = π y_{0}$

The frequency of the sinusoidal wave $y = 0 .40 \cos [2000 t + 0 .80 x]$ would be :
(1) 1000 π Hz
(2) 2000 Hz
(3) 20 Hz
(4) $\frac{1000}{π} H z$

A simple harmonic progressive wave is represented by the equation : $y = 8 \sin 2 π (0 .1 x - 2 t)$ where x and y are in cm and t is in seconds. At any instant the phase difference between two particles separated by 2.0 cm in the x-direction is :
(1) 18°
(2) 36°
(3) 54°
(4) 72°

A wave equation that gives the displacement along y-direction is given by $y = 0 .001 \sin (100 t + x)$ where x and y are in meter and t is time in seconds. This represented a wave :
(1) Of frequency $\frac{100}{π}$ Hz
(2) Of wavelength one metre
(3) Traveling with a velocity of $\frac{50}{π}$ ms^–1 in the positive X-direction
(4) Traveling with a velocity of 100 ms^–1 in the negative X-direction

Two waves represented by the following equations are travelling in the same medium $y_{1} = 5 \sin 2 π (75 t - 0 .25 x)$ , $y_{2} = 10 \sin π (150 t - 0 .50 x)$
The intensity ratio I₁/I₂ of the two waves is :
(1) 1 : 2
(2) 1 : 4
(3) 1 : 8
(4) 1 : 16

Which of the following is not true for this progressive wave $y = 4 \sin 2 π (\frac{t}{0 .02} - \frac{x}{100})$ where y and x are in cm and t in sec
(1) Its amplitude is 4 cm
(2) Its wavelength is 100 cm
(3) Its frequency is 50 cycles/sec
(4) Its propagation velocity is 50 × 10³ cm/sec

The phase difference between two waves represented by $y_{1} = 10^{- 6} \sin [100 t + (x / 50) + 0 .5] m,$ $y_{2} = 10^{- 6} \cos [100 t + (x / 50)] m$ where x is expressed in metres and t is expressed in seconds, is approximately:
(1) 1.5 rad
(2) 1.07 rad
(3) 2.07 rad
(4) 0.5 rad

A particle on the trough of a wave at any instant will come to the mean position after a time (T = time period)
(1) T/2
(2) T/4
(3) T
(4) 2T

10.

If the equation of the transverse wave is Y = 2sin(kx – 2t), then the maximum particle velocity is :
1. 4 units
2. 2 units
3. 0
4. 6 units

11.

Two sound waves (expressed in CGS units) given by $y_{1} = 0 .3 \sin \frac{2 π}{λ} (v t - x)$ and $y_{2} = 0 .4 \sin \frac{2 π}{λ} (v t - x + θ)$ interfere. The resultant amplitude at a place where the phase difference is π/2 will be :
(1) 0.7 cm
(2) 0.1 cm
(3) 0.5 cm
(4) $\frac{1}{10} \sqrt{7} c m$

12.

The amplitude of a wave represented by displacement equation $y = \frac{1}{\sqrt{a}} \sin ω t \pm \frac{1}{\sqrt{b}} \cos ω t$ will be
(1) $\frac{a + b}{a b}$
(2) $\frac{\sqrt{a} + \sqrt{b}}{a b}$
(3) $\frac{\sqrt{a} \pm \sqrt{b}}{a b}$
(4) $\sqrt{\frac{a + b}{a b}}$

13.

A wave represented by the given equation $y = a \cos (k x - ω t)$ is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is :
(1) $y = a \sin (k x + ω t)$
(2) $y = - a \cos (k x + ω t)$
(3) $y = - a \cos (k x - ω t)$
(4) $y = - a \sin (k x - ω t)$

14.

A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 Å between them. The wavelength of the standing wave is :
1. 1.21 Å
2. 2.42 Å
3. 6.05 Å
4. 3.63 Å

15.

In stationary waves, the distance between a node and its nearest antinode is 20 cm. The phase difference between two particles having a separation of 60 cm will be :
(1) Zero
(2) π/2
(3) π
(4) 3π/2

16.

A standing wave is represented by
$Y = A \sin (100 t) \cos (0 .01 x)$
where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of the wave is :
(1) 10⁴ m/s
(2) 1 m/s
(3) 10^–4m/s
(4) Not derivable from the above data

17.

The stationary wave produced on a string is represented by the equation $y = 5 \cos (π x / 3) \sin 40 π t$ where x and y are in cm and t is in seconds. The distance between consecutive nodes is :
1. 5 cm
2. π cm
3. 3 cm
4. 40 cm

18.

A string is rigidly tied at two ends and its equation of vibration is given by $y = (\cos 2 π t) (\sin 2 π x)$ Then minimum length of the string is :
1. 1 m
2. $\frac{1}{2} m$
3. 5 m
4. 2π m

19.

An empty vessel is getting filled with water, then the frequency of vibration of the air column in the vessel
(1) Remains the same
(2) Decreases
(3) Increases
(4) First increases then decrease

20.

A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude $ρ_{0}$ inside the tube. If the atmospheric pressure is $ρ_{A}$ , then the ratio of maximum and minimum pressure at the closed end of the tube will be :
1. $\frac{(ρ_{A} + ρ_{0})}{(ρ_{A} - ρ_{0})}$
2. $\frac{(ρ_{A} + 2 ρ_{0})}{(ρ_{A} - 2 ρ_{0})}$
3. $\frac{ρ_{A}}{ρ_{A}}$
4. $\frac{(ρ_{A} + \frac{1}{2} ρ_{0})}{(ρ_{A} - \frac{1}{2} ρ_{0})}$

21.

An open pipe of length l vibrates in the fundamental mode. The pressure variation is maximum at :
(1) l/4 from ends
(2) The middle of the pipe
(3) The ends of the pipe
(4) At l/8 from ends of pipe

22.

In a closed organ pipe, the frequency of the fundamental note is 50 Hz. The note of which of the following frequencies will not be emitted by it :
(1) 50 Hz
(2) 100 Hz
(3) 150 Hz
(4) None of the above

23.

What is the base frequency if a pipe gives notes of frequencies 425, 255 and 595 and decide whether it is closed at one end or open at both ends :
(1) 17, closed
(2) 85, closed
(3) 17, open
(4) 85, open

24.

Two closed organ pipes of length 100 cm and 101 cm 16 beats in 20 sec. When each pipe is sounded in its fundamental mode calculate the velocity of sound
(1) 303 ms^–1
(2) 332 ms^–1
(3) 323.2 ms^–1
(4) 300 ms^–1

25.

An open tube is in resonance with string (frequency of vibration of the tube is n₀). If the tube is dipped in water so that 75% of the length of the tube is inside water, then the ratio of the frequency of tube to string now will be :
(1) 1
(2) 2
(3) $\frac{2}{3}$
(4) $\frac{3}{2}$

26.

The frequency of a whistle of an engine is 600 cycles/sec is moving with the speed of 30 m/sec towards an observer. The apparent frequency will be (velocity of sound = 330 m/s)
(1) 600 cps
(2) 660 cps
(3) 990 cps
(4) 330 cps

27.

A source of sound is travelling with a velocity 40 km/hour towards the observer and emits the sound of frequency 2000 Hz. If the velocity of sound is 1220 km/hour, then what is the apparent frequency heard by an observer
1. 2210 Hz
2. 1920 Hz
3. 2068 Hz
4. 2086 Hz

28.

A source of sound and listener are approaching each other with a speed of 40 m/s. The apparent frequency of note produced by the source is 400 cps. Then, its true frequency (in cps) is (velocity of sound in air = 360 m/s)
1. 420
2. 360
3. 400
4. 320

29.

A man sitting in a moving train hears the whistle of the engine. The frequency of the whistle is 600 Hz
1. The apparent frequency as heard by him is smaller than 600 Hz
2. The apparent frequency is larger than 600 Hz
3. The frequency as heard by him is 600 Hz
4. None of the above

30.

A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f₁. If the train’s speed is reduced to 17 m/s, the frequency registered is f₂. If the speed of sound is 340 m/s then the ratio f₁/f₂ is
(1) 18/19
(2) 1/2
(3) 2
(4) 19/18

31.

If source and observer both are relatively at rest and if speed of sound is increased then frequency heard by observer will :
(1) Increases
(2) Decreases
(3) Can not be predicted
(4) Will not change

32.

A source and an observer move away from each other with a velocity of 10 m/s with respect to ground. If the observer finds the frequency of sound coming from the source as 1950 Hz, then actual frequency of the source is (velocity of sound in air = 340 m/s)
(1) 1950 Hz
(2) 2068 Hz
(3) 2132 Hz
(4) 2486 Hz

33.

A whistle revolves in a circle with an angular speed of 20 rad/sec using a string of length 50 cm. If the frequency of sound from the whistle is 385 Hz, then what is the minimum frequency heard by an observer, which is far away from the centre in the same plane ? $(v_{s o u n d} = 340 m / s)$
(1) 333 Hz
(2) 374 Hz
(3) 385 Hz
(4) 394 Hz

34.

A Siren emitting sound of frequency 800 Hz is going away from a static listener with a speed of 30 m/s, frequency of the sound to be heard by the listener is (take velocity of sound as 330 m/s)
(1) 733.3 Hz
(2) 644.8 Hz
(3) 481.2 Hz
(4) 286.5 Hz

35.

A car sounding a horn of frequency 1000 Hz passes an observer. The ratio of frequencies of the horn noted by the observer before and after the passing of the car is 11 : 9. If the speed of sound is v, the speed of the car is
(1) $\frac{1}{10} v$
(2) $\frac{1}{2} v$
(3) $\frac{1}{5} v$
(4) v

36.

A small source of sound moves on a circle as shown in the figure and an observer is standing on O. Let n₁, n₂ and n₃ be the frequencies heard when the source is at A, B, and C respectively. Then

(1) n₁ > n₂ > n₃
(2) n₂ > n₃ > n₁
(3) n₁ = n₂ > n₃
(4) n₂ > n₁ > n₃

37.

A source emits a sound of frequency of 400 Hz, but the listener hears it to be 390 Hz. Then
(1) The listener is moving towards the source
(2) The source is moving towards the listener
(3) The listener is moving away from the source
(4) The listener has a defective ear

38.

The difference between the apparent frequency of a source of sound as perceived by an observer during its approach and recession is 2% of the natural frequency of the source. If the velocity of sound in air is 300 m/sec, the velocity of the source is : (It is given that velocity of source << velocity of sound)
(1) 6 m/sec
(2) 3 m/sec
(3) 1.5 m/sec
(4) 12 m/sec

39.

A source producing the sound of frequency 170 Hz is approaching a stationary observer with a velocity of 17 ms^–1. The apparent change in the wavelength of sound heard by the observer is (speed of sound in air = 340 ms^–1)
1. 0.1m
2. 0.2m
3. 0.4m
4. 0.5m

40.

An observer moves towards a stationary source of sound with a speed 1/5^th of the speed of sound. The wavelength and frequency of the sound emitted are λ and f respectively. The apparent frequency and wavelength recorded by the observer are respectively :
1. $1.2 f, λ$
2. $f, 1 .2 λ$
3. $0.8 f, 0 .8 λ$
4. $1 .2 f, 1 .2 λ$

41.

The equation of displacement of two waves are given as $y_{1} = 10 \sin (3 π t + \frac{π}{3})$ ; $y_{2} = 5 (\sin 3 π t + \sqrt{3} \cos 3 π t)$ . Then what is the ratio of their amplitudes ?
1. 1 : 2
2. 2 : 1
3. 1 : 1
4. None of these

42. An organ pipe that is closed at one end has a fundamental frequency of $1500~\text{Hz}$. The maximum number of overtones generated by this pipe that a normal person can hear is:

1.	$14$	2.	$13$
3.	$6$	4.	$9$

43.

The correct graph between the frequency n and square root of density (ρ) of wire, keeping its length, radius and tension constant, is :
(1)
(2)
(3)
(4)

44.

If the speed of the wave shown in the figure is 330m/s in the given medium, then the equation of the wave propagating in the positive x-direction will be (all quantities are in M.K.S. units) :

(1) $y = 0 .05 \sin 2 π (4000 t - 12 .5 x)$
(2) $y = 0 .05 \sin 2 π (4000 t - 122 .5 x)$
(3) $y = 0 .05 \sin 2 π (3300 t - 10 x)$
(4) $y = 0 .05 \sin 2 π (3300 x - 10 t)$

45.

A wave motion has the function $y = a_{0} \sin (ω t - k x)$ . The graph in figure shows how the displacement y at a fixed point varies with time t. Which one of the labeled points shows a displacement equal to that at the position $x = \frac{π}{2 k}$ at time t = 0

(1) P
(2) Q
(3) R
(4) S

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1.	\(14\)	2.	\(13\)
3.	\(6\)	4.	\(9\)

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