Question

Two sinusoidal waves in a string are defined by the wave functions

y_{1} |
= | 1.60
sin (15.0 − 33.0x)t |

y_{2} |
= | 1.60
sin (28.0 − 42.0x)t |

where *x*, *y*_{1}, and
*y*_{2} are in centimeters and *t* is in
seconds.

(a) What is the phase difference between these two waves at the
point *x* = 5.00 cm at *t* = 2.00 s? (Your answer
should be between 0° and 360°.)

Your response differs from the correct answer by more than 10%.
Double check your calculations.°

(b) What is the positive *x* value closest to the origin for
which the two phases differ by ±*π* at *t* = 2.00 s?
(At that location, the two waves add to zero.)

The correct answer is not zero. cm

Answer #1

Two transverse sinusoidal waves combining in a medium are
described by the wave functions y1 = 1.00 sin π(x + 0.500t) y2 =
1.00 sin π(x − 0.500t) where x, y1, and y2 are in centimeters and t
is in seconds. Determine the maximum transverse position of an
element of the medium at the following positions. (a) x = 0.130 cm
|ymax| = ? (b) x = 0.460 cm |ymax| = ? (d) Find the three smallest
values of x...

Two waves on one string are described by the wave functions
y1 = 2.5 cos(4.5x −
1.3t)
y2 = 4.5 sin(5.5x − 1.5t)
where x and y are in centimeters and
t is in seconds. Find the superposition of the waves
y1 + y2 at the following
points. (Remember that the arguments of the trigonometric functions
are in radians.)
(a) x = 1.00, t = 1.00
cm
(b) x = 1.00, t = 0.500
cm
(c) x = 0.500, t...

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.

Consider two sinusoidal sine waves traveling along a string,
modeled as
y1(x, t) = (0.4 m)sin[(7
m−1)x − (5 s−1)t]
and
y1(x, t) = (0.4 m)sin[(7
m−1)x + (5 s−1)t].
What is the wave function of the resulting wave? (Hint: Use the
trig identity
sin(u ± v) = sin(u) cos(v) ±
cos(u) sin(v).
Use the following as necessary: x and t.
Assume x and y are measured in meters and
t is measured in seconds. Do not include units in...

Two waves are described by
y1 = 0.24 sin[π(3x -
180t)]
and
y2 = 0.24 sin[π(3x -
180t) + π/4],
where y1, y2, and
x are in meters and t is in seconds. When these
two waves are combined, a traveling wave is produced. What are the
(a) amplitude, (b) wave speed,
and (c) wavelength of that traveling wave?

These two waves travel along the same string: y1 = (4.17 mm)
sin(2.24?x - 300?t), y2 = (5.96 mm) sin(2.24?x - 300?t +
0.727?rad). What are (a) the amplitude and (b) the phase angle
(relative to wave 1) of the resultant wave? (c) If a third wave of
amplitude 5.20 mm is also to be sent along the string in the same
direction as the first two waves, what should be its phase angle in
order to maximize the amplitude...

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 are described by y1 = 0.21 sin[?(9x - 190t)] and y2 =
0.21 sin[?(9x - 190t) + ?/4], where y1, y2, and x are in meters and
t is in seconds. When these two waves are combined, a traveling
wave is produced. What are the (a) amplitude, (b) wave speed, and
(c) wavelength of that traveling wave?

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:...

These two waves travel along the same string: y1 = (4.37 mm)
sin(2.17πx - 440πt) y2 = (5.75 mm) sin(2.17πx - 440πt +
0.754πrad).
What are (a) the amplitude and
(b) the phase angle (relative to wave 1) of the
resultant wave? (c) If a third wave of amplitude
5.45 mm is also to be sent along the string in the same direction
as the first two waves, what should be its phase angle in order to
maximize the amplitude...

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