Question

Two waves traveling in opposite directions on a stretched rope
interfere to give the standing wave described by the following wave
function:

y(x,t) = 4 sin(2πx) cos(120πt),

where, y is in centimetres, x is in meters, and t is in seconds.
The rope is two meters long, L = 2 m, and is fixed at both
ends.

In terms of the oscillation period, T, at which of the following times would all elements on the string have a zero vertical displacement, y(x,t) = 0, for the first time:

t = T/8

t = T/4

t = T/2

t = 3T/4

t = T

Other:

If the oscillation frequency is decreased by a factor of four, f_new = f/4, while keeping the tension force, the length of the rope, and the linear mass density constants, then how many loops would appear on the rope?

One loop

Two loops

Three loops

Four loops

No loops appear, because the conditions are not satisfied for the standing waves to exist.

Other:

The wave functions of two waves traveling in the same direction
are given below. The two waves have the same frequency, wavelength,
and amplitude, but they differ in their phase constant.

y1 (x,t) = 2 sin(2πx ‒ 20πt), and

y2 (x,t) = 2 sin(2πx ‒ 20πt + φ),

where, y is in centimetres, x is in meters, and t is in
seconds.

Which of the following wave functions represents the resultant wave due to the interference between the two waves:

y_result (x,t) = 4 sin(2πx ‒ 20πt + φ)

y_result (x,t) = 2 sin(πx ‒ 10πt + φ/2)

y_result (x,t) = 4 cos(φ/2) cos(πx ‒ 10πt - φ/2)

y_result (x,t) = 4 cos(φ/2) sin(2πx ‒ 20πt + φ/2)

y_result (x,t) = 2 sin(φ/2) sin(2πx ‒ 20πt + φ/2)

Other:

If the amplitude of the resultant wave is A_res = 2 cm, then which of the following values of φ is correct:

π/6

π/3

π/2

2π/3

π

Other:

The speed of the resultant wave due to the interference between y_1 and y_2 is:

80π cm/s

10 m/s

20 m/s

80π cos(φ/2) cm/s

0.1 m/s

Other:

Assume that the two waves start to propagate at the same instant, t_0,1 = t_0,2 = 0 sec, but at different initial positions from an observation point. Wave-1 travels a distance x1 to get to the observation point, while wave-2 travels a distance x2. The amplitude of the resultant wave due to interference would be maximum at the observation point if the path difference between the two waves, ∆x=x2-x1, is:

π m

4 cm

1.5 m

0.5 m

1 m

Other:

Answer #1

Dear student as per guide lines we have to solve only one question. Please like and support.

The wave functions of two waves traveling in the same
direction are given below. The two waves have the same frequency,
wavelength, and amplitude, but they differ in their phase
constant.
y1 (x,t) = 2 sin(2πx ‒ 20πt), and
y2 (x,t) = 2 sin(2πx ‒ 20πt + φ),
a)where, y is in centimetres, x is in meters, and t is
in seconds.
Which of the following wave functions represents the
resultant wave due to the interference between the two waves:...

Two waves moving in opposite directions produce a standing wave.
The individual wave functions are: y1(x, t) = 5 sin (5x – 10t)
y2(x, t) = 5 sin (5x + 10t) where x and y are in meters and t in
seconds.
A. What is the amplitude of the simple harmonic motion of the
element of the medium located at x = 5 m?
B. What is the position of the first anti-node if one end of the
string is...

Two waves traveling on a string in the same direction both have
a frequency of 100 Hz, a wavelength of 2 cm, and an amplitude of
0.02 m. What is the amplitude of the resultant wave if the original
waves differ in phase by each of the following values?
(a) π/6 cm
(b) π/3

The following two traveling waves are superposed to create a
standing wave:
phi1 = (2.7 cm)sin((1.45 cm^-1)x - (9.7 s^-1)t)
phi2 = (2.7 cm)sin((1.45 cm^-1)x + (9.7 s^-1)t)
a) what is the resulting amplitude of the standing wave?
b) what is the resulting wavelength of the standing wave?
c) what is the resulting angular frequency of the standing
wave?

Two waves traveling on a string in the same direction both have
a frequency of 269 Hz, a wavelength of 0.29 m,
and an amplitude of 0.44 m. What is the amplitude of the
resultant wave if the original waves differ in phase by π/3
rad?
Tries 0/10
What is the phase difference between the two waves if the
amplitude of the resultant wave is 0.22 m?

Is it possible for two waves traveling in the same direction to
interfere and produce a wave with an amplitude larger than either
of the two initial waves?
A.Yes. This is an example of destructive
interference.
B.No. It is impossible for two waves heading in the same
direction to interfere with each other.
C.No. Waves cannot combine and will bend to pass around each
other if they meet at a point.
D. Yes. This is an example of constructive
interference.

Two waves are generated on a string of length 5.1 m to produce a
three-loop standing wave with an amplitude of 5.0 cm. The wave
speed is 119 m/s. Let the equation for one of the waves be of the
form y(x, t) = ym sin
(kx + ωt). In the equation for the other wave,
what are (a) ym,
(b) k, (c) ω,
and (d) the sign in front of ω?

Two waves in one string are described by the wave functions y1=
(6 cm)sin (5x- 1.6t) and y2 = (6 cm) sin (5x +1.6t+π/2). Find the
superposition of waves and name of the resultant wave. Also
determine the wave speed, amplitude of the reusltant wave.

1.). Two sinusoidal waves are moving through a medium in the
same direction, both having amplitudes of 4.00 cm, a wavelength of
3.50 m, and a period of 6.25 s, but one has a phase shift of an
angle φ. What is the phase shift (in rad) if the resultant
wave has an amplitude of 4.00 cm? Hint: Use the trig identity
2.). Consider two sinusoidal sine waves traveling along a
string, modeled as
y1(x, t) = (0.2 m)sin[(6 m−1)x...

A transverse harmonic wave travels on a rope according to the
following expression: y(x,t) = 0.14sin(2.7x + 17.5t) The mass
density of the rope is ? = 0.147 kg/m. x and y are measured in
meters and t in seconds.
What is the amplitude of the wave?
What is the frequency of oscillation of the wave?
What is the wavelength of the wave?
What is the tension in the rope?
At x = 3.1 m and t = 0.43 s,...

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