The equation of a plane wave travelling along positive direction of x-axis is y = asin 2 π λ ( νt – x ) When this wave is reflected at a rigid surface and its amplitude becomes 80 % , then find the equation of the reflected wave

New amplitude of the reflected wave a ' = 80 % a = 0 . 8 a . After reflection, phase of the wave changes by π . Thus, the path difference in the reflected wave will be ∆ x = λ 2 π π = λ 2 . After the reflection, the wave will be travelling in negative x direction. Hence, the equation of reflected wave is y R = 0 . 8 a sin 2 π λ ν t + x + λ 2 .

EASY

JEE Main/Advance

IMPORTANT

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In the arrangement shown in figure, the string has mass of $5 g$ . How much time will it take for a transverse disturbance produced at the floor to reach the pulley $A$ ? Take $g = 10 m / s^{2}$ .

Important Questions on Wave Motion on a String

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 1>Q 25

A uniform rope of length

20 m

and mass

8 kg

hangs vertically from a rigid support. A block of mass

2 kg

is attached to the free end of the rope. A transverse pulse of wavelength

0.06 m

is produced at the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope?

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 1>Q 26

A particle on a stretched string supporting a travelling wave takes minimum time

5.0 ms

to move from its mean position to the mean position. The distance between two consecutive particles, which are at their mean positions, is

2.0 cm

. Find the frequency, the wavelength and the wave speed.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 1>Q 28

4.0 kg

block is suspended from the ceiling of an elevator through a string having a linear mass density of

1.6 \times 10^{- 3} kg / m

. Find (a) speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of

6 m / s^{2}

. (b) In part (a) at some instant speed of lift is

40 m / s

in upward direction, then speed of the wave pulse with respect to ground at that instant is (Take

g = 10 m / s^{2}

)

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 1>Q 29

6.00 m

segment of a long string has a mass of

180 g

. A high-speed photograph shows that the segment contains four complete cycles of a wave. The string is vibrating sinusoidally with a frequency of

50.0 Hz

and a peak-to-valley displacement of

15.0 cm

. (The “peak-to-valley” displacement is the vertical distance from the farthest positive displacement to the farthest negative displacement.) (a) Write the function that describes this wave traveling in the positive x direction. (b) Determine the average power being supplied to the string.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 1>Q 30

A transverse wave of amplitude

5 mm

and frequency

10 Hz

is produced on a wire stretched to a tension of

100 N

. If the wave speed is

100 m s^{- 1}

, what average power is the source transmitting to the wire?

(π^{2} = 10)

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 1>Q 31

The equation of a plane wave travelling along positive direction of x-axis is

y = asin \frac{2 π}{λ} (νt - x)

When this wave is reflected at a rigid surface and its amplitude becomes

80 %

, then find the equation of the reflected wave

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 1>Q 33

Two waves, each having a frequency of

100 Hz

and a wavelength of

2 cm

, are travelling in the same direction on a string. What is the phase difference between the waves (a) if the second wave was produced

10 ms

later than the first one at the same place (b) if the two waves were produced at a distance

1 cm

behind the second one? (c) If each of the waves has an amplitude of

2.0 mm

, what would be the amplitudes of the resultant waves in part (a) and (b)?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 1>Q 37

A string oscillates according to the equation,
$y^{'} = (0.80 cm) \sin [(\frac{π}{3} {cm}^{- 1}) x] \cos [(40 π s^{- 1}) t]$
What is the

$(a)$ amplitude

$(b)$ speed of the two waves (identical except the direction of travel) whose superposition gives this oscillation?

$(c)$ What is the distance between nodes?

$(d)$ What is the transverse speed of a particle of the string at the position $x = 2.1 cm$ when $t = 0.50 s$ ?

In the arrangement shown in figure, the string has mass of 5g. How much time will it take for a transverse disturbance produced at the floor to reach the pulley A ? Take g = 10 m/s2.

Important Questions on Wave Motion on a String

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In the arrangement shown in figure, the string has mass of $5 g$ . How much time will it take for a transverse disturbance produced at the floor to reach the pulley $A$ ? Take $g = 10 m / s^{2}$ .