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Q. No.A travelling wave is set up on a stretched string. If the tension in the string is increased by \(1\%,\) then the percentage change in the transverse wave velocity on the string is:
1.
\(0.5\%\)
2.
\(1\%\)
3.
\(2\%\)
4.
\(1.5\%\)
Subtopic: Travelling Wave on String |
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The displacement of a particle in a medium due to a wave traveling in the \(x\)-direction is given by the equation: \(y = A\sin(\alpha t -\beta x),\)
where \(t\) represents time, and \(\alpha\) and \(\beta\) are constants. Identify the correct statements.
| (A) | The frequency of the wave is \(\alpha.\) |
| (B) | The frequency of the wave is \(\dfrac{\alpha}{2 \pi}.\) |
| (C) | The wavelength is \(\dfrac{2\pi}{\beta}.\) |
| (D) | The velocity of the wave is \(\dfrac{\alpha}{\beta}.\) |
Choose the correct option from the given ones:
| 1. | (A), (B) and (C) only |
| 2. | (A) and (B) only |
| 3. | (B) and (D) only |
| 4. | (B), (C) and (D) only |
Subtopic: Wave Motion |
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The given, equation describes a wave:
\(y=A~\text{sin}314\bigg[{\Large\frac{t}{0.5~\text s}}-{\Large\frac{x}{100~\text m}}\bigg].\)
Identify the correct relationships regarding its frequency \(n\) and wavelength \(\lambda.\)
(A) \(n = 2~\text{Hz}\)
(B) \(n = 100~\text{Hz}\)
(C) \(\lambda= 2~\text m\)
(D) \(\lambda= 100~\text m\)
Choose the correct option from the given ones:
| 1. | (A), (B) and (C) only |
| 2. | (A) and (B) only |
| 3. | (B) and (C) only |
| 4. | (B), (C) and (D) only |
Subtopic: Wave Motion |
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A transverse sinusoidal wave of amplitude \(A,\) wavelength \(\lambda,\) and frequency \(f\) is travelling along a stretched string. The maximum speed of any point on the string is \(\dfrac{v}{10},\) where \(v\) is the speed of propagation of the wave. Given that \(A = 10 ^{-3}~\text m \) and \(v = 10~\text{m/s} ,\) the values of \(\lambda\) and \(f\) are:
Choose the correct option from the given ones:
| (A) | \(\lambda=2\pi\times10^{-2}~\text m \) |
| (B) | \(\lambda=10^{-3}~\text m \) |
| (C) | \(f=\dfrac{10^3}{2\pi}~\text{Hz}\) |
| (D) | \(f=10^3~\text{Hz} \) |
| 1. | (A), (B) and (C) only |
| 2. | (A) and (C) only |
| 3. | (B) and (D) only |
| 4. | (B), (C) and (D) only |
Subtopic: Wave Motion |
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Which of the following statements are true for a stationary wave?
Choose the correct option:
1. (a), (c)
2. (a), (b), (d), (e)
3. (b), (d)
4. (c), (d)
| (a) | Every particle has a fixed amplitude which is different from the amplitude of its nearest particle. |
| (b) | All the particles cross their mean position at the same time. |
| (c) | All the particles are oscillating with same amplitude. |
| (d) | There is no net transfer of energy across any plane. |
| (e) | There are some particles which are always at rest. |
1. (a), (c)
2. (a), (b), (d), (e)
3. (b), (d)
4. (c), (d)
Subtopic: Standing Waves |
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Speed of sound waves in a fluid depends upon
Choose the correct option:
| (a) | directly on density of the medium. |
| (b) | square of Bulk modulus of the medium. |
| (c) | inversly on the square root of density. |
| (d) | directly on the square root of bulk modulus of the medium. |
Choose the correct option:
| 1. | (a), (c) | 2. | (a), (b), (c) |
| 3. | (b), (d) | 4. | (c), (d) |
Subtopic: Speed of Sound |
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The displacement of a string is given by \(y (x,t) = 0.06 ~\sin (2πx/3) ~\cos (120πt) \) where \(x\) and \(y\) are in m and \(t\) in s. The length of the string is \(1.5\) m and its mass is \(3.0\times 10^{-2}~\text{kg}\).
Choose the correct option from the given ones:
1. (A), (C)
2. (A), (B), (C)
3. (B), (C)
4. (D) only
| (A) | It represents a progressive wave of frequency \(60\) Hz. |
| (B) | It represents a stationary wave of frequency \(60\) Hz. |
| (C) | It is the result of the superposition of two waves of wavelength \(3\) m, frequency \(60\) Hz each travelling with a speed of \(180\) m/s in opposite directions. |
| (D) | The amplitude of this wave is constant. |
Choose the correct option from the given ones:
1. (A), (C)
2. (A), (B), (C)
3. (B), (C)
4. (D) only
Subtopic: Standing Waves |
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A string of mass \(2.5~\text{kg}\) is under a tension of \(200~\text N.\) The length of the stretched string is \(20.0~\text m.\) If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in:
| 1. | \(1\) second |
| 2. | \(0.5\) second |
| 3. | \(2\) seconds |
| 4. | The data given is insufficient |
Subtopic: Travelling Wave on String |
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Sound waves of wavelength \(\lambda\) travelling in a medium with a speed of \(v\) m/s enter into another medium where its speed is \(2v\) m/s. Wavelength of sound waves in the second medium is:
1. \(\lambda \)
2. \(\dfrac{\lambda}{2} \)
3. \(2 \lambda \)
4. \(4 \lambda\)
1. \(\lambda \)
2. \(\dfrac{\lambda}{2} \)
3. \(2 \lambda \)
4. \(4 \lambda\)
Subtopic: Speed of Sound |
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The displacement of a traveling wave is given by \(y=C\sin\dfrac{2\pi}{\lambda}({at}-x)\) where \(t\) is time, \(x\) is distance and \(\lambda\) is the wavelength, all in SI units. The frequency of the wave is:
| 1. | \(\dfrac{2\pi\lambda}{a}\) | 2. | \(\dfrac{2\pi a}{\lambda}\) |
| 3. | \(\dfrac{\lambda}{a}\) | 4. | \(\dfrac{a}{\lambda}\) |
Subtopic: Wave Motion |
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NEET - 2024
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