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Consider a traveling wave described by the formula

$y_1(x,t) = A \sin(k x - \omega t)$ .

This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.

Part A

Which one of the following statements about the wave described in the problem introduction is correct?

ANSWER:

The wave is traveling in the

direction.
The wave is traveling in the

direction.
The wave is oscillating but not traveling.
The wave is traveling but not oscillating.

Part B

Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0

this new wave should have the same displacement as y_1(x,t)

, the wave described in the problem introduction.

ANSWER:

$A \cos (k x - \omega t)$
$A \cos (k x + \omega t)$
$A \sin (k x - \omega t)$
$A \sin (k x + \omega t)$

The principle of superposition states that if two functions each separately satisfy the wave equation, then the sum (or difference) also satisfies the wave equation. This principle follows from the fact that every term in the wave equation is linear in the amplitude of the wave.

Consider the sum of two waves , where is the wave described in Part A and is the wave described in Part B. These waves have been chosen so that their sum can be written as follows:

$y_{\rm s}(x,t) = y_{\rm e}(x) y_{\rm t}(t)$ .

This form is significant because , called the envelope, depends only on position, and depends only on time. Traditionally, the time function is taken to be a trigonometric function with unit amplitude; that is, the overall amplitude of the wave is written as part of .

Part C
Find and . Keep in mind that should be a trigonometric function of unit amplitude.

erinhyena808

Two Velocities in a Traveling Wave

Wave motion is characterized bytwo velocities: the velocity with which the wave moves in themedium (e.g., air or a string) and the velocity of the medium (theair or the string itself).

Consider a transverse wavetraveling in a string. The mathematical form of the wave is

$y(x,t) = A \sin(kx-\omega t)$

Part A

Find the velocity of propagation v_p of this wave.

Express the velocity of propagation in terms of some or all of the variables A, k,and w.

Part B

Find the y velocity v_y(x,t) of a point on the string as a function of x and t.

Express the y velocity in terms of w, A,k,x,and t.

Part C

Which of the following statements about, the x component of the velocity of the string, is true?

a) v_x(x;t) = v_p

b) v_x(x;t) = v_y(x;t)

c) v_x(x;t) has the same mathematical form as v_y(x;t) but is 180° out of phase.

d) v_x(x;t) = 0

magentaelephant622

Please solve this as early as possible.

(1). Light waves are electromagnetic waves that traval at 3. 00 x 10^8 m/s. The aye Is most sensitive to light having a wavelength of 5. 50 x 10^-7m. {a} Find the frequency of this light wave Hz =

Find the frequency of this light wave (HZ)
and its period(S).

2.The distance between two successive minima of a transverse wave is 3.00 m. Five full crest Intervals of the wave pass given point along the direction of travel every

14.2 s.

(a) Find the frequency of the wave Hz

(b} Find the wave speed m/s
3.
A harmonic wave bs traveling slong a repe It is observed that the oscillator that generates the wave completes 36.0 vibrations In 35.0 s Also, a given maximum travels 430 cm along the rope in 9.0 s What Is the wavelength in cm ?
4.
A bat can detect small objects, such as an insect, whose size is approximately equal to one wavelength of the sound the bat makes. If bats emit a chirp at a Frequency of

8.54 x 10^4 Hz, and if the speed of sound in air is 343 m/s, what is the smallest Insect a bat can detect in mm ?
5. A cork on the surface of 5 pond bobs up and down two times per second an Hippies having a wavelength of 9.50 cm .If the cork is 11.5 m fram shore, how long does it take a tipple passing the cork to reach the shore ?
( )S.

6. Ocean waves are traveling te the east at 4. 7 m/s with a distance of 19 m between crests. (a) With what frequency do the waves hit the front of a boat when the boat Is at anchor?
( ) HZ

(b) With what frequency do the waves hit the front of a boat when the boat Is moving westward at 1.5 m/s?
( ) HZ

A circus performer stretches s tightrope between two towers. He strikes ane end of the rope and sends a wave atong it toward the other tower He notes that It takes the

wave 0. 840 s to reach the opposite tower, 20.0 m away If s 1.00-m length of the rope has a mass of 0.260 kg, find the tension In the tightrope .
( ) N ?.

8. Transverse waves with a speed of 52. 0 m/s are to be produced on a stretched string A 5 .20-m length of string with a total mass of 0.0600 kg Is used.

{a) What is the required tension in the string?
( )N
(b} Calculate the wave speed in the string if the tension Is 8. 00 N.
( )m/s . ?

9.A wave of amplitude 0 .53 m interferes with a second wave of amplitude 0 .19 m traveling in the same direction.

(a) What Is the largest resultant amplitude that can occur, and under what conditions will this maximum arise?

( ) m

1.The two waves interfere destructively,

2.The two waves interfere constructively.

(b) What is the smallest resultant amplitude that cah occur, and under what conditions will this minimum arise?
( ) m

1.The two waves interfere destructively

2.The two waves interfere constructively

10.

A certain tuning fork vibrates at a frequency of 161 Hz while each tip of Its two prongs has an amplitude of 0. 724 mm .

(a) What ts the per od of this motlon?
( )ms .

(b) Find the wavelength of the sound produced by the vibrating fork taking the speed of sound in alr to be 343 m/s.
( ) m .

manya12

Physics 1402A/B Lecture Notes - Lecture 29: Longitudinal Wave

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