Waves Difficult Questions and Answers | Page - 3

Waves

A uniform rope of length L and mass m1 hangs vertically from a rigid support. A block of mass m₂ is attached to the free end of the rope. A transverse pulse of wavelength λ₁ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is λ₂ the ratio λ₂/λ₁ is

1. √ m₁
  m₂
1. √ m₁ + m₂
  m₂
1. √ m₂
  m₁
1. √ m₁ + m₂
  m₁

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From figure, tension T₁ = m₂g
T₂ = (m₁ + m₂)g
As we know
Velocity ∝ √T So,
λ ∝ √T
⇒ λ₁ = √T₁
λ₂ √T₂

⇒ λ₂ = √ m₁ - m₂
λ₁ m₂

Correct Option: B

From figure, tension T₁ = m₂g
T₂ = (m₁ + m₂)g
As we know
Velocity ∝ √T So,
λ ∝ √T
⇒ λ₁ = √T₁
λ₂ √T₂

⇒ λ₂ = √ m₁ - m₂
λ₁ m₂

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is :

1. 66.7 cm
1. 100 cm
1. 150 cm
1. 200 cm

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For a closed organ pipe first minimum resonating length
L₁ = λ/4 = 50 cm
∴ Next or second resonating length, L₂
= 3λ/4 = 150 cm.

Correct Option: C

For a closed organ pipe first minimum resonating length
L₁ = λ/4 = 50 cm
∴ Next or second resonating length, L₂
= 3λ/4 = 150 cm.

The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?

1. 20 Hz
1. 30 Hz
1. 40 Hz
1. 10 Hz

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Difference in two successive frequencies of closed pipe 2v/4l = 260 – 220 = 40 Hz
or 2v/4l = 40 Hz
⇒ v/4l = 20Hz
Which is the fundamental frequency of system of closed organ pipe.

Correct Option: A

Difference in two successive frequencies of closed pipe 2v/4l = 260 – 220 = 40 Hz
or 2v/4l = 40 Hz
⇒ v/4l = 20Hz
Which is the fundamental frequency of system of closed organ pipe.

The velocity of sound in any gas depends upon

1. wavelength of sound only
1. density and elasticity of gas
1. intensity of sound waves only
1. amplitude and frequency of sound

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Velocity of sound in any gas depends upon density and elasticity of gas.

Correct Option: B

Velocity of sound in any gas depends upon density and elasticity of gas.

The transverse wave represented by the equation
y + 4sin π sin(3x + 15t) has
6

1. amplitude = 4
1. wavelength = 4(π/3)
1. speed of propagation = 5
1. period = π/15

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Compare the given equation with standard form
y = r sin 2πx - 2πt
λ T

2π = 3,λ = 2π and 2π = 15
λ 3 T

T = 2π
15

Speed of propagation,
v = λ = 2π/3 = 5
T 2π/15

Correct Option: C

Compare the given equation with standard form
y = r sin 2πx - 2πt
λ T

2π = 3,λ = 2π and 2π = 15
λ 3 T

T = 2π
15

Speed of propagation,
v = λ = 2π/3 = 5
T 2π/15