1. The equation of the propagating wave is \[Y =25\sin \left(20t+5x\right)\] where y is displacement.
Which of the following statement is not true
a) The amplitude of the wave is 25 units
b) The wave is propagating in positive x -
direction
c) The velocity of the wave is 4 units
d) The maximum velocity of the particles is 500
units
Explanation: Positive sign in the argument of sin indicating that wave is travelling in negative x-direction.
2. In a plane progressive wave given by \[Y =25\cos \left(2\pi t-\pi x\right)\] , the amplitude and frequency
are respectively
a)25,100
b) 25, 1
c) 25 ,2
d) \[50\pi ,2\]
Explanation:
3. The displacement y of a wave travelling in the xdirection
is given by \[Y =10^{-4}\sin \left(600 t-2 x+\frac{\pi}{3}\right)\]
metres, where x is expressed in metres and t in
seconds. The speed of the wave-motion, in \[ms^{-1}\] , is
a) 200
b) 300
c) 600
d) 1200
Explanation:
4. The displacement y of a particle in a medium can
be expressed as: \[Y =10^{-6}\sin \left(100 t+20 x+\pi/4\right)m\]
,where t is in second and x in meter. The speed of
wave is
a) 2000 m/s
b) 5 m/s
c) 20 m/s
d) \[5 \pi\] m/s
Explanation:
5. If the wave equation \[Y =0.08\sin\frac{2 \pi}{\lambda} \left(200 t- x\right)\]
then
the velocity of the wave will be
a) \[400 \sqrt{2}\]
b) \[200 \sqrt{2}\]
c) 400
d) 200
Explanation:
6. The phase difference between two points
separated by 0.8 m in a wave of frequency is 120
Hz is \[\frac{\pi}{2}\] . The velocity of wave is
a) 720 m/s
b) 384 m/s
c) 250 m/s
d) 1 m/s
Explanation:
7. A plane progressive wave is represented by the
equation \[Y =0.1\sin \left(200\pi t- \frac{20\pi x}{17}\right)\]
where y is displacement in
m, t in second and x is distance from a fixed
origin in meter. The frequency, wavelength and
speed of the wave respectively are
a) 100 Hz, 1.7 m, 170 m/s
b) 150 Hz, 2.4 m, 200 m/s
c) 80 Hz, 1.1 m, 90 m/s
d) 120 Hz, 1.25 m, 207
m/s
Explanation: Comparing the given equation with standard equation
8.The equation of a travelling wave is given by \[Y =0.5\sin \left(20x- 400 t\right)\] where x and y are in meter
and t is in second. The velocity of the wave is
a) 10 m/s
b) 20 m/s
c) 200 m/s
d) 400 m/s
Explanation:
9.A transverse progressive wave on a stretched
string has a velocity of 10 m \[s^{-1}\] and a frequency of
100 Hz. The phase difference between two
particles of the string which are 2.5 cm apart will
be
a) \[\frac{\pi}{8}\]
b) \[\frac{\pi}{4}\]
c) \[\frac{3\pi}{8}\]
d) \[\frac{\pi}{2}\]
Explanation:
10.A transverse sinusoidal wave of amplitude a,
wavelength \[\lambda\] and frequency n is travelling on a
stretched string. The maximum speed of any point
on the string is v/10, where v is the speed of
propagation of the wave. If \[a=10 ^{-3}\] and
\[v=10 ms^{-1}\] , then \[\lambda\] and n are given by
a) \[\lambda =2\pi\times 10^{-2}m\]
b) \[\lambda = 10^{-3}m\]
c) \[n = \frac{10^{3}}{2\pi} Hz\]
d) Both a and c
Explanation:
