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Q. No.A stretched wire of length \(1~\text{m},\) under an initial tension, vibrates with a fundamental frequency of \(256~\text{Hz}.\) When the tension in the wire is increased by \(1~\text{kg-wt},\) the fundamental frequency becomes \(320~\text{Hz}.\) What is the initial tension in the wire?
1.
\(\dfrac{3}{4}~\text{kg-wt}\)
2.
\(\dfrac{4}{3}~\text{kg-wt}\)
3.
\(\dfrac{16}{9}~\text{kg-wt}\)
4.
\(\dfrac{20}{9}~\text{kg-wt}\)
Subtopic: Travelling Wave on String |
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The vibrations of four air columns under identical conditions are shown in the figure below. The ratio of their frequencies \(n_p: n_q: n_r: n_s\) will be:
| 1. | \(12:6:3:4\) | 2. | \(1:2:4:3\) |
| 3. | \(4:2:3:1\) | 4. | \(6:2:3:4\) |
Subtopic: Standing Waves |
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Which of the following expressions represents a wave?
| 1. | \(y=A \sin (\omega t-kx)\) |
| 2. | \(y=A \cos ^2(a t-bx+c)+A \sin ^2(at-bx+c)\) |
| 3. | \(y=A \sin kx\) |
| 4. | \(y=A \sin \omega t\) |
Subtopic: Types of Waves |
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The fundamental frequency of vibration of a wire fixed at both ends is \(120~\text{Hz}.\) The wire can also vibrate in harmonics. The possible frequencies are:
| 1. | \(60~\text{Hz},40~\text{Hz},30~\text{Hz},...\) |
| 2. | \(240~\text{Hz},360~\text{Hz},480~\text{Hz},...\) |
| 3. | \(240~\text{Hz},300~\text{Hz},360~\text{Hz},...\) |
| 4. | \(180~\text{Hz},240~\text{Hz},300~\text{Hz},...\) |
Subtopic: Beats |
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When a travelling wave is reflected off a fixed end, the reflected wave has:
| 1. | the same frequency |
| 2. | a lower frequency |
| 3. | a higher frequency |
| 4. | a higher or a lower frequency |
Subtopic: Wave Motion |
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A string, under tension, and lying along the \(x\)-axis is set into transverse vibrations. The displacement at a point \(x\) is given by the function \(y(x,t)\) where \(t\) represents the time: \(y(x,t)=\left ( 3~\text{mm} \right )\mathrm{sin}\left ( \frac{\pi x}{20~\text{cm}} \right ) \)\(\mathrm{cos}\left\{2\pi\left ( 100~\text{s}^{-1} \right )t \right\}\)
The maximum amplitude of vibration at any point on the string is:
1. \(3~\text{mm}\)
2. \(20~\text{cm}\)
3. \(300~\text{mm}\)
4. \(15~\text{mm}\)
The maximum amplitude of vibration at any point on the string is:
1. \(3~\text{mm}\)
2. \(20~\text{cm}\)
3. \(300~\text{mm}\)
4. \(15~\text{mm}\)
Subtopic: Standing Waves |
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A sinusoidal waveform whose displacement is given by:
\(y(x,t)=(5~\text{mm})\sin2\pi\)\(\large{\Big(\frac{x}{2~\text{m}}+\frac{t}{0.01~\text s}\Big)}\)
propagates along the \(x\)-axis. The wavelength of the waveform is:
\(y(x,t)=(5~\text{mm})\sin2\pi\)\(\large{\Big(\frac{x}{2~\text{m}}+\frac{t}{0.01~\text s}\Big)}\)
propagates along the \(x\)-axis. The wavelength of the waveform is:
| 1. | \(\large\frac{2\pi}{2}\)\(~\text m\) | 2. | \(\large\frac{1}{2}\)\(~\text m\) |
| 3. | \(\large\frac{2}{2\pi}\)\(~\text m\) | 4. | \(2~\text m\) |
Subtopic: Wave Motion |
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A transverse wave is described by the equation:
\(y=A \sin2 \pi\left(n t-x / \lambda_0\right) \)
If the maximum particle velocity is three times the wave velocity, then the wavelength \(\lambda_0=\)
| 1. | \(\dfrac{\pi A}{3}\) | 2. | \(\dfrac{2 \pi A}{3}\) |
| 3. | \(\pi A\) | 4. | \(3 \pi A\) |
Subtopic: Wave Motion |
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A wave is described by the equation \( x=4 \cos \left(8 t-\dfrac{y}{2}\right) ,\) where \(x\) and \(y\) are in metres, and \(t\) is in seconds. The frequency of the wave (in \(\text{s}^{-1}\)) is:
| 1. | \(\dfrac{4}{\pi}\) | 2. | \(\dfrac{8}{\pi}\) |
| 3. | \(\dfrac{2}{\pi}\) | 4. | \(\dfrac{\pi}{4}\) |
Subtopic: Wave Motion |
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If the fundamental frequency of the string is \(220~ \text{cps}\), the frequency of its fifth harmonic will be:
| 1. | \(44~\text{cps}\) | 2. | \(55~\text{cps}\) |
| 3. | \(1100~\text{cps}\) | 4. | \(440~\text{cps}\) |
Subtopic: Travelling Wave on String |
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Level 1: 80%+
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