Single Choice

the equation of a progressive wave is given by $$y=5$$ sin $$(100\pi t-0.4\pi x)$$ where $$y$$ and $$x$$ are in $$m$$ and $$t$$ is in $$s$$. (1) The amplitude of the wave is $$5$$ $$m$$. (2) The wavelength of the wave is $$5$$ $$m$$. (3) The frequency of the wave is $$50$$ $$Hz$$. (4) The velocity of the wave is $$250$$ $$m/s$$Which of the following statement are correct?

A(1), (2) and (3)
B(2) and (3)
C(1) and (4)
DAll are correct
Correct Answer

Solution

the equation of a given progressive wave is
$$y=5 sin (100\pi t-0.4\pi x)$$ ......(i)
The standard equation of a progressive wave is
$$y= a sin (\omega t- Kx)$$ ...(ii)
Comparing (i) and (ii), we get

$$a= 5 m,\omega = 100\pi$$ rad $$s^{-1},k= o.4\pi m^{-1}$$

(1) Amplitude of the wave, $$a=5 m$$

(2) Wavelength of the wave, $$\lambda =\dfrac { 2\pi }{ k } =\dfrac { 2\pi }{ 0.4\pi } =5m$$

(3)Frequency of the wave, $$\upsilon =\dfrac { \omega }{ 2\pi } =\dfrac { 100\pi }{ 2\pi } =50\quad Hz$$

(4) Velocity of the wave, $$\nu =\upsilon \lambda =(50 s^{-1}) (5 m)$$

$$=250 m s^{-1}$$

SIMILAR QUESTIONS

Physical World

A wave is represented by the equation, $$y=(0.001mm)\sin[(50s^{-1})t+(2m^{-1})x]$$

Physical World

The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by $$y = (0.4 cm ) \sin [(0.314 cm^{-1}) x ] \cos [(600 \pi s^{-1}) t]$$. What is the frequency of vibration.

Physical World

A transverse harmonic wave on a string is described by $$y(x, t) =3.0 sin (36 t+0.018x+\pi /4 )$$ where x and y are in cm and t in s. The positive direction of x is from left to right. (a) Is this a travelling wave or a stationary wave? If it is travelling what are the speed and direction of its propagation? (b) What are its amplitude and frequency? (c) What is the initial phase at the origin? (d) What is the least distance between two successive crests in the wave?

Physical World

If a transmission line in a cold climate collects ice, the increased diameter tends to cause vortex formation in a passing wind. The air pressure variations in the vortexes tend to cause the line to oscillate (gallop), especially if the frequency of the variations matches a resonant frequency of the line. In long lines, the resonant frequencies are so close that almost any wind speed can set up a resonant mode vigorous enough to pull down support towers or cause the line to short out with an adjacent line. If a transmission line has a length of $$ 347 \mathrm{m}, $$ a linear density of $$ 3.35 \mathrm{kg} / \mathrm{m}, $$ and a tension of $$ 65.2 \mathrm{MN} $$, what are the frequency of the fundamental mode

Physical World

A generator at one end of a very long string creates a wave given by $$y=(6.0 \mathrm{cm}) \cos \dfrac{\pi}{2}\left[\left(2.00 \mathrm{m}^{-1}\right) x+\left(8.00 \mathrm{s}^{-1}\right) t\right]$$ and a generator at the other end creates the wave $$y=(6.0 \mathrm{cm}) \cos \dfrac{\pi}{2}\left[\left(2.00 \mathrm{m}^{-1}\right) x-\left(8.00 \mathrm{s}^{-1}\right) t\right]$$ Calculate the frequency of each wave.

Physical World

A string along which waves can travel is 2.70 m long and has a mass of 260 g. The tension in the string is 36.0 N. What must be the frequency of traveling waves of amplitude 7.70 mm for the average power to be 85.0 W?

Physical World

A wave has a speed of $$ 240 \mathrm{m} / \mathrm{s} $$ and a wavelength of $$ 3.2 \mathrm{m} . $$ What is the frequency?

Physical World

The equation of a transverse wave traveling along a string is $$y=(2.0 \mathrm{mm}) \sin \left[\left(20 \mathrm{m}^{-1}\right) x-\left(600 \mathrm{s}^{-1}\right) t\right]$$ Find the frequency?

Physical World

The speed of electromagnetic waves (which include visible light, radio, and $$ x $$ rays ) in vacuum is $$ 3.0 \times 10^{8} \mathrm{m} / \mathrm{s} $$. Wavelengths of visible light waves range from about $$ 400 \mathrm{nm} $$ in the violet to about $$ 700 \mathrm{nm} $$ in the red. What is the range of frequencies of these waves?

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