# Sinusoidal Wave

## Trending Questions

**Q.**For a given wave , maximum particle velocity is 5 times the wave velocity corresponding to the equation,

y=Asin(5t−0.05x) in which A , x are in metres and t is in seconds. The value of A is

**Q.**The equation for a wave travelling in x direction on a string is given as

y=10sin(πt−0.5x), where y and x are in m and time(t) in sec. Find the acceleration of a particle at x=π m at time t=1 sec.

- −10π m/s2
- 5π m/s2
- −10π2 m/s2
- −5π m/s2

**Q.**When a sound wave of wavelength λ is propagating in a medium, the maximum velocity of the particle is equal to the wave velocity. The amplitude of wave is:

- λ2
- λ
- λ4π
- λ2π

**Q.**

The equation of a transverse wave travelling on a rope is given by y=10sin π(0.001x−2.00t) where y and x are in centimeters and t in seconds. The maximum transverse speed of a particle in the rope is about.

121 cm/s

63 cm/s

100 cm/s

75 cm/s

**Q.**

The equation of a transverse wave travelling on a rope is given by y=10sin π(0.001x−2.00t) where y and x are in centimeters and t in seconds. The maximum transverse speed of a particle in the rope is about.

63 cm/s

75 cm/s

100 cm/s

121 cm/s

**Q.**

Why a transverse wave can be either mechanical or non-mechanical wave ?

**Q.**Equation of a plane progressive wave is given by y=0.6sin2π(t−x2). On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is

- y=−0.4sin2π(t+x2)
- y=0.6sin2π(t+x2)
- y=−0.4sin2π(t−x2)
- y=0.4sin2π(t+x2)

**Q.**A long wire PQR is made by joining two wires PQ and QR of equal radii. PQ has length 4.8 m and mass 0.06 kg. QR has length 2.56 m and mass 0.2 kg. The wire PQR is under a tension of 80 N. A sinusoidal wave-pulse of amplitude 3.5 cm is sent along the wire PQ from the end P. No power is dissipated during the propagation of the wave-pulse. Calculate the time taken (in s) by the wave pulse to reach the other end R of the wire.

**Q.**Poynting vectors →S is defined as a vector whose magnitude is equal to the wave intensity and whose direction is along the direction of wave propagation.

Mathematically, it is given by →S=1μ0(→E×→B).

Show the nature of S vs t graph.

**Q.**Which of the following function correctly represent the travelling wave equation for finite values of x and t?

- y=x2−t2
- y=log(x2−t2)−log(x−t)
- y=e2xsint
- y=cosx2sint

**Q.**A wave pulse, travelling on a two-piece string, gets partially reflected and partially transmitted at the junction. The reflected wave is inverted in shape as compared to the incident one. If the incident wave has wavelength λ and transmitted wave λ'. Then

- λ'<λ
- λ'=λ
- λ'>λ
- None

**Q.**

When a wave travels in a medium, the particle displacement is given by

y(x, t)=0.03 sin π(2t−0.01x)

where y and x are expressed in metres and t in seconds. At a given instant of time, the phase difference between two particles 25 m apart is

π8

π4

π2

π

**Q.**The phenomena involved in the reflection of radio waves by ionosphere is similar to or not as the total internal reflection of light in air during a mirage.

**Q.**A transverse wave on a string has an amplitude of 0.2 m and a frequency of 175 Hz. Consider a particle of the string at x = 0. It begins with a displacement y = 0, at t = 0, according to equation y=0.2 sin (kx±ωt). How much time passes between the first two instant when this particle has a displacement of y = 0.1 m?

- 0.5 ms
- 2.4 ms
- 1.9 ms
- 3.9 ms

**Q.**

Figure (15-E2) shows a plot of the transverse displacements of the particles of a string at t = 0 through which a travelling wave is passing in the positive x-direction. The wave speed is 20 cm s−1. Find (a) the amplitude, (b) the wavelength, (c) the wave number and (d) the frequency of the wave.

**Q.**

As the wavelength of a wave in a uniform medium increases, then what will happen with its speed?

**Q.**

Simplify the expression $1-{\mathrm{sin}}^{2}x$

**Q.**A sound signal is sent through a composite tube as shown in the figure. The radius of the semicircle is R and speed of sound in air is v. If 'n' is an integer, then the frequencies of the signal for obtaining maximum value of intensity are given by

- nv(R−2)π
- nvπR
- nvR
- nvR(π−2)

**Q.**In the equation representing wave function,

y=Asin(kx−ωt+ϕ0)

The term phase is defined as:

- ϕ0
- ϕ0−ωt
- kx+ϕ0
- kx−ωt+ϕ0

**Q.**Graph shows three waves that are separately sent along a string that is stretched under a certain tension along x-axis. If ω1, ω2 and ω3 are their angular frequencies, respectively, then:

**Q.**Angular frequency is defined as the rate of change of angular displacement.

- True
- False

**Q.**For the equation, y=Asin2π(ax+bt+π/4), match the following columns.

Column IColumn II(A) Frequency of wave(Hz)(p) a(B) wavelength of wave(m)(q) b(C) Phase difference between two points 14a m distance apart(r) π(D) Phase difference of a particle after a time interval of 18b s(s) π2(t) None of above

- ABCDqtst
- ABCDtqrs
- ABCDpqrs
- ABCDtspr

**Q.**The maximum acceleration of a particle in a sinusoidal wave is (symbols have their usual meaning)

- Aω
- Aω2
- Aω3
- Aω4

**Q.**The equation of a wave is y(x, t)=0.1sin[π3(10x−30t)−π6] m.

Find the acceleration of the particle at x=0.85 m and t=0.25 s

[Assume, π2=10 ; ↑ denotes positive y−direction and ↓ denotes negative y−direction ]

- 40 m/s2 ↑
- 50 m/s2 ↓
- 40 m/s2 ↓
- 50 m/s2 ↑

**Q.**

The equation for a standing wave generated by a string, with both ends fixed, is$y=(0.4cm)\mathrm{sin}(0.314c{m}^{-1})x]\mathrm{cos}[\left(600\mathrm{\xcf\u20ac}{s}^{\xe2\u02c6\u20191}\right)t].$. Figure out the smallest length of the string.

**Q.**If vibration frequency f of the star is given by the following equation: f=KRaPbGc where R is the radius of star, ρ is the density of star, G is the universal gravitational constant and kis a constant, then (b+c)is equal to

**Q.**In interference of two waves, two individual amplitudes are A0 each and the intensity is I0 each. The resultant amplitude at a point where phase difference between two waves is 60∘ is

- √2A0
- √3A0
- A0
- 2A0

**Q.**

Figure (16-E12) shows a source of sound moving along the X-axis at a speed of 22 m s−1 continuously emitting a sound of frequency 2.0 kHz which travels in air at a speed of 330 m s−1. A listener Q stands on the Y-axis at a distance of 330 m from the origin. At t = 0, the source crosses the origin P. (a) When does the sound emitted from the source at P reach the listener Q ? (b) What will be the frequency heard by the listener at this instant? (c) Where will the source be at this instant ?

**Q.**Write the equation of the wave shown in figure, if its position is shown at t=0.6 sec. The wavelength is 15 cm and amplitude is 4 cm and the crest X was at x=0 at t=0.

- y(x, t)=(2 cm)sin[(1.68 rad/s)t−(1 cm−1)x]
- y(x, t)=sin[(3.2 rad/s)t−(0.42 cm−1)x]
- y(x, t)=(2 cm)cos[(3.2 rad/s)t−(0.42 cm−1)x]
- y(x, t)=(4 cm)cos[(1.68 rad/s)t−(0.42 cm−1)x]

**Q.**Two sinusoidal waves are defined by the functions :

y1=(2.00 cm) sin (20x−32t) and y2=(2.00 cm) sin (25x−40t) where y1, y2 and x are in centimeters and t is in seconds. What is the phase difference between these two waves at the point x=5.00 cm at t=2 s?

- 516∘
- 258∘
- 333∘
- 412∘