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A rope of total mass m and length L is suspended vertically. Analysis shows that for a short transverse pulse, the wave above a short distance from the free end of the rope can be represented to a good approximation by the linear wave equation. 

Show that a transverse pulse travels the length of the rope in a time interval that is given approximately by . Suggestion: First find an expression for the wave speed at any point a distance x from the lower end by considering the rope's tension as resulting from the weight segment below that point. 

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John Edward Cayas
John Edward CayasLv10
15 Nov 2020

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A rope of total mass m and length L is suspended vertically. A pulse travels from the bottom to the top of the rope in an approximate time interval with a speed that varies with position x measured from the bottom of the rope as . Assume the linear wave equation describes waves at all locations on the rope. (a) Over what time interval does pulse travel halfway up the rope? Give your answer as a fraction of the quantity . (b)  A pulse starts traveling up the rope. How far has it traveled after a time interval ?

  1. 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

7.

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 .

  1. Please solve all questions  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

7. 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 motion?
(          )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 .

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