Question

Four waves are to be sent along the same string, in the same direction y1(x,t) = (2 mm) sin(2px – 200pt)

y2(x,t) = (2 mm) sin(2px – 200pt + 0.7p) y3(x,t) = (2 mm) sin(2px – 200pt + p) y4(x,t) = (2 mm) sin(2px – 200pt + 3.7p)

(a) For y1, what is the (a) frequency, (b) wavelength and (c) speed? When these waves are all added together, what is the (d) amplitude of the resultant wave?

Answer #1

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...

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...

These two waves travel along the same string:
y1 = (3.59 mm) sin(2.23πx
- 380πt)
y2 = (5.61 mm) sin(2.23πx
- 380πt + 0.861πrad).
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
5.21 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...

These two waves travel along the same string:
y1 = (4.14 mm) sin(2.31πx
- 430πt)
y2 = (5.79 mm) sin(2.31πx
- 430πt + 0.771πrad).
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
5.24 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...

These two waves travel along the same string:
y1 =
(3.73 mm) sin(1.60πx -
340πt)
y2 =
(5.39 mm) sin(1.60πx - 340πt +
0.867πrad).
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
4.89 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...

These two waves travel along the same string:
y1 = (4.57 mm)
sin(2.24πx - 320πt)
y2 = (5.81 mm)
sin(2.24πx - 320πt +
0.800π 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
4.93 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...

Two sinusoidal waves of the same frequency are to be sent in the
same direction along a taut string. One wave has an amplitude of
6.7 mm, the other 10.2 mm. (a) What phase
difference φ1 between the two waves results in
the smallest amplitude of the resultant wave? (b)
What is that smallest amplitude? (c) What phase
difference φ2 results in the largest amplitude
of the resultant wave? (d) What is that largest
amplitude? (e) What is the resultant...

Two sinusoidal waves of the same frequency are to be sent in the
same direction along a taut string. One wave has an amplitude of
6.2 mm, the other 8.5 mm. (a) What phase
difference φ1 between the two waves results in
the smallest amplitude of the resultant wave? (b)
What is that smallest amplitude? (c) What phase
difference φ2 results in the largest amplitude
of the resultant wave? (d) What is that largest
amplitude? (e) What is the resultant...

Two sinusoidal waves, identical except for phase, travel in the
same direction along a string, producing a net wave y´(x, t) =
(1.90 mm) sin(22.0x - 6.80t + 0.940 rad), with x in meters and t in
seconds. What are (a) the wavelength λ of the two waves, (b) the
phase difference between them, and (c) their amplitude ym?

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.

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