The displacement of a particle is given by , where x is in metres and t is in seconds. The velocity of the wave is:
1. 5000 m/sec
2. 2 m/sec
3. 0.5 m/sec
4. 300 m/sec
The equation \(y(x,t) = 0.005 ~cos (\alpha x- \beta t)\) describes a wave traveling along the x-axis. If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then and in appropriate units are:
1.
2.
3.
4.
If a travelling wave pulse is given by \(y=\frac{20}{4+(x+4 t)^2}~\text{m}\), then:
1. | the pulse is traveling along the negative x axis. |
2. | the speed of the pulse is \(4\) m/s. |
3. | the amplitude of the pulse is \(5\) m. |
4. | all of these. |
The equation of a progressive wave is given by .
Which of the following is correct?
1. v = 5 m / sec
2. λ = 18 m
3. a = 0.04 m
4. n = 50 Hz
A wave traveling in the +ve \(x\)-direction having maximum displacement along \(y\)-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. \( y=\sin (x-2 t)\)
If a wave is travelling in a positive X-direction with A = 0.2 m, velocity = 360 m/s, and λ = 60 m, then the correct expression for the wave will be:
1. | \(\mathrm{y}=0.2 \sin \left[2 \pi\left(6 \mathrm{t}+\frac{\mathrm{x}}{60}\right)\right]\) |
2. | \(\mathrm{y}=0.2 \sin \left[ \pi\left(6 \mathrm{t}+\frac{\mathrm{x}}{60}\right)\right]\) |
3. | \(\mathrm{y}=0.2 \sin \left[2 \pi\left(6 \mathrm{t}-\frac{\mathrm{x}}{60}\right)\right]\) |
4. | \(\mathrm{y}=0.2 \sin \left[ \pi\left(6 \mathrm{t}-\frac{\mathrm{x}}{60}\right)\right]\) |
The wave described by y=0.25 sin(10), where x and y are in metres and t in seconds, is a wave traveling along the:
1. | -ve x direction with frequency 1 Hz |
2. | +ve x direction with frequency π Hz and wavelength λ =0.2 m |
3. | +ve x direction with frequency 1 Hz and wavelength λ = 0.2 m |
4. | - ve x direction with amplitude 0.25 m and wavelength λ = 0.2 m |
Given the equation for a wave on the string, y = 0.5 sin(5x - 3t) where y and x are in metres and t in seconds, the ratio of the maximum speed of particle to the speed of wave is:
1. | 1:1 | 2. | 5:2 |
3. | 3:2 | 4. | 4:5 |
1. | wave \(C\) lags behind in phase by \(\pi/2\) and wave \(B\) leads by \(\pi/2\). |
2. | wave \(C\) leads in phase by \(\pi\) and wave \(B\) lags behind by \(\pi\). |
3. | wave \(C\) lags behind in phase by \(\pi/2\) and wave \(B\) leads behind by \(\pi\). |
4. | wave \(C\) lags behind in phase by \(\pi\) and wave \(B\) leads by \(\pi\). |