Question

Two waves in one string are described by the wave functions y1= (6 cm)sin (5x- 1.6t)...

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.

Homework Answers

Answer #1

So superposition of this two waves is given by,

y = y1+ y2

So,

y=  (6 cm)sin (5x- 1.6t) + (6 cm)sin(5x+1.6t+π/2)

Or we can write second term as

y=  (6 cm)sin (5x- 1.6t) + (6 cm)cos(5x+1.6t)

So from the formula of

sinx + cosy = 2sin(x+y/2) cos(x-y/2)

So from this we get

y = (12cm) sin(5x+π/4) cos(1.6t-π/4)

So as we can see wave speed is given by,

= Freaquany* wavelength

But the wave represent a standing wave for that case it will not travel in medium so wave velocity should be zero

And Amplitude of wave as you can see

A = 12 cm

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Two waves on one string are described by the wave functions y1 = 2.5 cos(4.5x −...
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 on one string are described by the wave functions y1 = 2.5 cos(3.5x −...
Two waves on one string are described by the wave functions y1 = 2.5 cos(3.5x − 1.3t) y2 = 3.5 sin(4.5x − 2.5t), where x and y are in centimeters and t is in seconds. Find the values 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 (b) x = 1.00, t = 0.500 (c) x = 0.500, t = 0
Two transverse sinusoidal waves combining in a medium are described by the wave functions y1 =...
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 are described by y1 = 0.24 sin[π(3x - 180t)] and y2 = 0.24 sin[π(3x...
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?
Two sinusoidal waves in a string are defined by the wave functions y1 = 1.60 sin...
Two sinusoidal waves in a string are defined by the wave functions y1 = 1.60 sin (15.0x − 33.0t) y2 = 1.60 sin (28.0x − 42.0t) where x, y1, and y2 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%....
These two waves travel along the same string: y1 = (4.37 mm) sin(2.17πx - 440πt) y2...
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...
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...
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...
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...
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...