When a string is divided into three segments of lengths l 1 , l 2 and l 3 the fundamental frequencies of these three segments are ν 1 , ν 2 and ν 3 respectively. The original fundamental frequency ν of the string is

1 ν = 1 ν 1 + 1 ν 2 + 1 ν 3

A travelling harmonic wave is represented by the equation y x , t = 10 - 3 sin 50 t + 2 x , where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave?

The wave is propagating along the negative x -axis with speed 25 m s - 1

The wave is propagating along the positive x -axis with speed 25 m s - 1

The wave is propagating along the positive x -axis with speed 100 m s - 1

The wave is propagating along the negative x -axis with speed 100 m s - 1

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A uniform rope of length $L$ and mass $m_{1}$ , hangs vertically from a rigid support. A block of mass $m_{2}$ is attached to the free end of the rope. A transverse pulse of wavelength $λ_{1}$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $λ_{2}$ . The ratio $\frac{λ_{2}}{λ_{1}}$ is:

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Important Questions on Wave Motion on a String

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Alpha Question Bank for Medical: Physics>Chapter 20 - Wave Motion on a String>Exercise-3>Q 14

Five sinusoidal waves have the same frequency

500 Hz

but their amplitudes are and the ratio

2 : \frac{1}{2} : \frac{1}{2} : 1 : 1

and their phase angles

0, \frac{π}{6}, \frac{π}{3}, \frac{π}{2}

and

π

respectively. The phase angle of resultant wave obtained by the superposition of resultant wave obtained by the superposition of these five waves is

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Alpha Question Bank for Medical: Physics>Chapter 20 - Wave Motion on a String>Exercise-3>Q 16

The transverse displacement

y (x, t)

of a wave on a string is given by,

y (x, t) = e^{- (a x^{2} + b t^{2} + 2 \sqrt{a b} x t)}

. This represents a

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Alpha Question Bank for Medical: Physics>Chapter 20 - Wave Motion on a String>Exercise-3>Q 17

A travelling wave represented by

y = a \sin (ω t - k x)

is superimposed on another wave represented by,

y = a \sin (ω t + k x)

. The resultant is

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Alpha Question Bank for Medical: Physics>Chapter 20 - Wave Motion on a String>Exercise-3>Q 18

Statement I Two longitudinal waves given by equation

y_{1} (x, t) = 2 a \sin (ω t - k x)

and

y_{2} (x, t) = a \sin (2 ω t - 2 k x)

will have equal intensity.

Statement II Intensity of waves of given frequency in same medium is proportional to square of amplitude only

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Alpha Question Bank for Medical: Physics>Chapter 20 - Wave Motion on a String>Exercise-3>Q 19

A uniform string of length

20 m

is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (Take,

g = 10 m s^{- 2}

)

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Alpha Question Bank for Medical: Physics>Chapter 20 - Wave Motion on a String>Exercise-3>Q 20

A heavy ball of mass

M

is suspended from the ceiling of a car by a light string of mass

m (m ≪ M) .

When the car is at rest, the speed of transverse waves in the string is

60 m s^{- 1}

. When the car has acceleration

a

, the wave-speed increases to

60.5 m s^{- 1}

. The value of

a

in terms of gravitational acceleration

g

is closed to:

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Alpha Question Bank for Medical: Physics>Chapter 20 - Wave Motion on a String>Exercise-3>Q 21

A string of length

1 m

and mass

5 g

is fixed at both ends. The tension in the string is

8 .0 N

. The string is set into vibration using an external vibrator of frequency

100 Hz

. The separation between successive nodes on the string is close to

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Alpha Question Bank for Medical: Physics>Chapter 20 - Wave Motion on a String>Exercise-3>Q 22

Equation of travelling wave on a stretched string of linear density

5 g m^{- 1}

y = 0.03 \sin (450 t - 9 x)

, where distance and time are measured in SI units. The tension in the string is:

Important Questions on Wave Motion on a String

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