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Q. No.A standing wave is formed by the superposition of two waves traveling in opposite directions. The transverse displacement is given by \(y(x,t)=0.5\sin\left(\frac{5\pi}{4}x\right) \cos(200\pi t).\) What is the speed of the traveling wave moving in the positive \(x\) direction?
\((x\) and \(t\) are in meters and seconds, respectively.)
1. \(180~\text{m/s}\)
2. \(160~\text{m/s}\)
3. \(120~\text{m/s}\)
4. \(90~\text{m/s}\)
Subtopic: Standing Waves |
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Level 1: 80%+
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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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Level 2: 60%+
NEET - 2024
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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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Level 1: 80%+
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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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Level 1: 80%+
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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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Most symphony orchestras tune to 'standard pitch', which has a frequency of \(440~\text{Hz}.\) During a tuning session, sound from the orchestra takes \(1.5~\text{s}\) to reach audience members who are seated \(500 ~\text m\) away. What is the wavelength of this 'standard pitch' sound?
| 1. | \(0.05~\text m\) | 2. | \(0.5~ \text m\) |
| 3. | \(0.75~\text m\) | 4. | \(1.5~\text m\) |
Subtopic: Speed of Sound |
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Ocean waves strike a beach once every \(4~\text{s},\) and the distance between successive wave crests is \(12~\text{m}.\) What is the velocity of the waves as they move toward the shore?
| 1. | \(3~\text {m/s}\) | 2. | \(4~\text {m/s}\) |
| 3. | \(12~\text {m/s}\) | 4. | \(48~ \text {m/s}\) |
Subtopic: Types of Waves |
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Two violinists are playing together, but they are slightly out of tune with each other. If one violinist plays a note at \(883\text{ Hz}\) and the other plays at \(879\text{ Hz} ,\) what beat frequency will be heard?
| 1. | \(2\text{ Hz}\) | 2. | \(4\text{ Hz}\) |
| 3. | \(881\text{ Hz}\) | 4. | \(1762\text{ Hz}\) |
Subtopic: Beats |
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Level 1: 80%+
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Match the terms in Column-I with their corresponding descriptions in Column-II based on their relationship to wave phenomena.
Codes:
| Column-I | Column-II | ||
| \(\mathrm{(A)}\) | Wavelength \((\lambda)\) | \(\mathrm{(P)}\) | \(v=\lambda\times f\) |
| \(\mathrm{(B)}\) | Frequency \((f)\) | \(\mathrm{(Q)}\) | maximum displacement from the equilibrium position |
| \(\mathrm{(C)}\) | Amplitude \((A)\) | \(\mathrm{(R)}\) | number of oscillations per second |
| \(\mathrm{(D)}\) | Speed of a wave \((v)\) | \(\mathrm{(S)}\) | inversely proportional to frequency |
| 1. | \(\mathrm{A\text- Q,B\text- P,C\text- S,D\text-R }\) |
| 2. | \(\mathrm{A\text-S ,B\text-R ,C\text-Q ,D\text-P }\) |
| 3. | \(\mathrm{A\text-Q ,B\text-R ,C\text-S ,D\text-P }\) |
| 4. | \(\mathrm{A\text- S,B\text-Q ,C\text-P ,D\text- R}\) |
Subtopic: Wave Motion |
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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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