Q. No.| 1. | \(\dfrac{2\pi\lambda}{a}\) | 2. | \(\dfrac{2\pi a}{\lambda}\) |
| 3. | \(\dfrac{\lambda}{a}\) | 4. | \(\dfrac{a}{\lambda}\) |
A wave traveling in the +ve \(x\text-\)direction having maximum displacement along \(y\text-\)direction as \(1~\text{m}\), wavelength \(2\pi~\text{m}\) and frequency of \(\frac{1}{\pi}~\text{Hz}\), is represented by:
| 1. | \(y=\sin (2 \pi x-2 \pi t)\) | 2. | \(y=\sin (10 \pi x-20 \pi t)\) |
| 3. | \(y=\sin (2 \pi x+2 \pi t)\) | 4. | \( y=\sin (x-2 t)\) |
The equation of a simple harmonic wave is given by \(y=3\sin \frac{\pi}{2}(50t-x)\) where \(x \) and \(y\) are in meters and \(t\) is in seconds. The ratio of maximum particle velocity to the wave velocity is:
| 1. | \(\frac{3\pi}{2}\) | 2. | \(3\pi\) |
| 3. | \(\frac{2\pi}{3}\) | 4. | \(2\pi\) |
\(y_2 = a\cos(\omega t+kx)~\text{m},\) where \(x\) is in meters and \(t\) in seconds. The phase difference between them is:
1. \(1.25\) rad
2. \(1.57\) rad
3. \(0.57\) rad
4. \(1.0\) rad
A transverse wave is represented by y = Asin(ωt -kx). At what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1. A/2
2. A
3. 2A
4. A
1. \(y =(0.02~\text{m})\sin(7.85x+1005t)\)
2. \(y =(0.02~\text{m})\sin(15.7x-2010t)\)
3. \(y =(0.02~\text{m})\sin(15.7x+2010t)\)
4. \(y =(0.02~\text{m})\sin(7.85x-1005t)\)
The wave described by \(y=0.25\sin (10\pi x-2\pi t)\), where \(x \) and \(y\) are in metre and \(t\) in second, is a wave travelling along the:
| 1. | –ve x-direction with frequency \(1\) Hz |
| 2. | +ve x-direction with frequency \(\pi\) Hz and wavelength \(\lambda=0.2\) m |
| 3. | +ve x-direction with frequency \(1\) Hz and wavelength \(\lambda=0.2\) m |
| 4. | –ve x-direction with amplitude \(0.25\) m and wavelength \(\lambda=0.2\) m |
A transverse wave propagating along the \(x\text-\)axis is represented by:
\(y(x,t)=8.0\sin\left(0.5\pi x-4\pi t-\frac{\pi}{4}\right)\), where \(x\) is in meters and \(t\) in seconds. The speed of the wave is:
1. \(4\pi\) m/s
2. \(0.5\) m/s
3. \(\frac{\pi}{4}\) m/s
4. \(8\) m/s
The phase difference between two waves, represented by
\(y_1= 10^{-6}\sin \left\{100t+\left(\frac{x}{50}\right) +0.5\right\}~\text{m}\)
\(y_2= 10^{-6}\cos \left\{100t+\left(\frac{x}{50}\right) \right\}~\text{m}\)
where \(x\) is expressed in metres and \(t\) is expressed in seconds, is approximate:
1. \(2.07~\text{radians}\)
2. \(0.5~\text{radians}\)
3. \(1.5~\text{radians}\)
4. \(1.07~\text{radians}\)
| 1. | \({y}=0.2 \sin \left[2 \pi\left(6{t}+\frac{x}{60}\right)\right]\) |
| 2. | \({y}=0.2 \sin \left[ \pi\left(6{t}+\frac{x}{60}\right)\right]\) |
| 3. | \({y}=0.2 \sin \left[2 \pi\left(6{t}-\frac{x}{60}\right)\right]\) |
| 4. | \(y=0.2 \sin \left[ \pi\left(6{t}-\frac{x}{60}\right)\right]\) |
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