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Find the resulting acceleration from a 300 N force that acts on an

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Find the resulting acceleration from a 300 N force that acts on an

    ** SOLUTIONS Jaquin’s Sections **

    SCI111 Homework Assignment #5

    (20 Points Total)

    Chapter 5

    1. A water wave has a frequency of 6 Hz and a wavelength of 3m.

     a. What is the period of these waves?

    This is a basic wave structure problem. We need only the relation that links the

    1frequency and period of a wave: . fT

    1fT

     111T0.167 s1f6 Hz6 s

    The period of this wave is 0.167 seconds.

     b. What is the wave velocity?

    This is a basic wave velocity problem. We need only the relation that links the frequency

    wavelength and velocity of a wave: . vf(

    1m 6 Hz3 m6 3 m18 vf(ss

    The velocity of this wave is 18 m/s.

    2. The lower limit for human hearing is usually considered to be 20 Hz. What is the corresponding wavelength for this frequency if the air temperature is 20.0 C?

    This is a wave velocity problem. We need the relation that links the frequency

    wavelength and velocity of a wave: . Additionally we need to use the speed of vf(

    ??m?0.6(?m;s(331 Csound in air at 20C : . This velocity works out to be 343 ;;vT?;sC(?(?~)??

    m/s at 20C.

    ** SOLUTIONS Jaquin’s Sections **

    SCI111 Homework Assignment #5

    (20 Points Total)

    (vf

    mm343 343 vss(17.15 m1f20 Hz20 s

    The wavelength of 20 Hz sound waves in 20C air is 17.15 meters.

4. The low range of frequencies used for medical applications is about 1,000,000 Hz. What

    is the wavelength of this frequency in air?

    This is a wave velocity problem just like the previous problem. We need the relation that

    links the frequency wavelength and velocity of a wave: . Additionally we need vf(

    to use the speed of sound in air at 20C (assumed temperature) :

    ??m?0.6(?m;s(331 C. This velocity works out to be 343 m/s at 20C. ;;vT?;sC(?(?~)??

    (vf

    mm343 343 v-4ss(3.4310 m0.343 mm61f110 Hz6110 s

    The wavelength of 1,000,000 Hz sound waves in 20C air is 0.343 millimeters.

5. How much time will elapse between seeing and hearing an even that happens 400.0 m

    away?

    dThis is a basic . Let’s assume that the air temperature is 20C, so that the speed of vt

    sound is the by now familiar 343 m/s. The distance is 400.0 m, so…

    ** SOLUTIONS Jaquin’s Sections **

    SCI111 Homework Assignment #5

    (20 Points Total)

    dvt

     d400.0 m t1.17 smv343 s

    The elapsed time between seeing and hearing is 1.17 seconds.

    6. An echo bounces from a building exactly 1.00 seconds after you honk your horn. How many feet away is the building if the air temperature is 20.0 C?

    dThis is another basic , but with the “echo” twist. The speed of sound is the by now vt

    familiar 343 m/s.

    dvt mdvt343 1.00 s343 ms

    The distance the sound wave traveled in 1 second is 343 meters. However, since the

    sound echoed off the building the building is only ? that distance or 171.5 meters away.

    In feet (1 m = 3.281 ft) the distance is 563 feet from the building.

    7. A submarine sends a sonar signal, which returns from another ship 2.250 s later. How far away is the other ship if the speed of sound in sea water is 1,530.0 m/s?

    dThis is yet another basic , but with the “echo” twist. The speed of sound is the vt

    1,530 m/s.

    dvt mdvt1,530 2.250 s3,442.5 ms

    ** SOLUTIONS Jaquin’s Sections **

    SCI111 Homework Assignment #5

    (20 Points Total)

    The distance the sound wave traveled underwater in 2.25 second is 3,344.5 meters. However, since the sound echoed off the ship the ship is only ? that distance or 1,721 meters away

    8. A student clicks underwater clicks two rocks together and makes a sound with a frequency of 600.0 Hz and a wavelength of 2.5 meters. What is the speed of this underwater sound?

    Like the first problem assigned, this is a basic wave velocity problem. We need only the

    relation that links the frequency wavelength and velocity of a wave: . vf(

    1m 600 Hz2.5 m600 2.5 m1,500 vf(ss

    The velocity of this wave is 1,500 m/s.

9. You see condensed steam expelled from a ship’s whistle 2.5 s before you hear the sound.

    If the air temperature is 20.0 C, how many meters are you from the ship?

    dThis is again another basic . The speed of sound is the by now familiar 343 m/s in vt

    air at 20C. The time is 2.5 s, so…

    dvt mdvt343 2.5 s857.5 ms

    The ship is 857.5 meters away.

    11. A tuning fork vibrates 440.0 times second, producing sound waves with a wavelength of 78.0 cm. What is the velocity of these waves?

    This is a straight forward problem. vf(

    cyclesm440.0 0.78 m343.2 vf(ss

    The velocity of these waves is 343.2 m/s.

    ** SOLUTIONS Jaquin’s Sections **

    SCI111 Homework Assignment #5

    (20 Points Total)

    12. The distance between the center of a condensation and the center of an adjacent rarefaction is 65.23 cm. If the frequency is 256.0 Hz, how fast are these waves moving?

    This is a problem with one complication. We need to recognize that the distance vf(

    between the center of a condensation and the center of an adjacent rarefaction of 65.23 cm

    represents only ?.

    m256.0 Hz20.6523 m334.0 ;;vf(s

    The velocity of these waves is 334 m/s.

    14. Sound from the siren of an emergency vehicle has a frequency of 750.0 Hz and moves with a velocity of 343.0 m/s. What is the distance from one condensation to the next? This is a straight forward problem where we need to solve for the wavelength of the vf(

    sound.

    (vf

    m 343 vs(0.457 mf750 Hz

    The distance from one condensation to the next is one wavelength and is equal to 0.457 m or

    mm msss45.7 cm. (Note the units ) m1 Hzs1 s

15. The following sound waves have what velocity?

     a. 20.0 Hz, of 17.15 m

    This is a straight forward vf( problem.

    m20.0 Hz17.15m343 vf(s

    The velocity of these waves is 343 m/s.

    ** SOLUTIONS Jaquin’s Sections **

    SCI111 Homework Assignment #5

    (20 Points Total)

     b. 200.0 Hz, of 1.715 m

    The velocity of these waves is also 343 m/s.

     c. 2,000.0 Hz, of 17.15 cm

    The velocity of these waves is also 343 m/s.

     d. 20,000.0 Hz, of 1.715 cm

    The velocity of these waves also 343 m/s.

17. A ship at sea sounds a whistle blast, and an echo returns from the coastal land 10.0 s later.

    How many km is it to the coastal land if the air temperature s 10.0C?

    dThis is a problem where we first need to determine the speed of sound in air at 10C. vt

    m?0.6(mmmm;s(v33110C3316337;ssssC((~)

    dv t

    mdvt33710 s3,370 ms

    The whistle blast travels a total distance of 3, 370 meters. Therefore the distance form the land

    mass is ? that distance or 1.685 kilometers.

    19. A 600.0 Hz sound has a velocity of 1,087 ft/s in the air and a velocity of 4,920.0 ft/s in water.

    Find the wavelength of this sound in (a) the air and (b) the water. This is a straight forward vf( problem where we need to solve for the wavelength of the

    sound.

    ** SOLUTIONS Jaquin’s Sections **

    SCI111 Homework Assignment #5

    (20 Points Total)

    (vf

    ft1,087 vs(In air 1.81 ft f600 Hz

    ft4,920 vsIn water ( 8.20 ftf600 Hz

    The wavelength of this sound in the air is 1.81 feet and in the water is 8.20 feet.

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