** 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
1
frequency and period of a wave: f  .
T
f 
1
T
T 
1
1
1


 0.167 s
1
f 6 Hz
6
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: v  f   .
1
m
v  f    6 Hz  3 m  6  3 m  18
s
s
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: v  f   . Additionally we need to use the speed of


m
0.6 

m 
sound in air at 20C : v  331    s   T  C  . This velocity works out to be 343
s  C 






m/s at 20C.
 
** SOLUTIONS Jaquin’s Sections **
SCI111 Homework Assignment #5
(20 Points Total)
v  f 
m
m
343
v
s 
s  17.15 m
  
1
f
20 Hz
20
s
343
The wavelength of 20 Hz sound waves in 20C 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: v  f   . Additionally we need
to use the speed of sound in air at 20C (assumed temperature) :


m
0.6 



m
v  331    s   T  C  . This velocity works out to be 343 m/s at 20C.
s  C 






 
v  f 
m
m
343
v
s 
s  3.43  10 -4 m  0.343 mm
  
f 1 10 6 Hz
6 1
1 10
s
343
The wavelength of 1,000,000 Hz sound waves in 20C air is 0.343 millimeters.
5. How much time will elapse between seeing and hearing an even that happens 400.0 m
away?
d
. Let’s assume that the air temperature is 20C, so that the speed of
t
sound is the by now familiar 343 m/s. The distance is 400.0 m, so…
This is a basic v 
** SOLUTIONS Jaquin’s Sections **
SCI111 Homework Assignment #5
(20 Points Total)
v
d
t
t 
d 400.0 m

 1.17 s
m
v
343
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?
This is another basic v 
d
, but with the “echo” twist. The speed of sound is the by now
t
familiar 343 m/s.
v
d
t
 d  v  t  343
m
1.00 s  343 m
s
The distance the sound wave traveled in 1 second is 343 meters. However, since the
sound echoed off the building the building is only ½ 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?
This is yet another basic v 
d
, but with the “echo” twist. The speed of sound is the
t
1,530 m/s.
v
d
t
 d  v  t  1,530
m
 2.250 s  3,442.5 m
s
** 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 ½ 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: v  f   .
1
m
v  f    600 Hz  2.5 m  600  2.5 m  1,500
s
s
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?
d
. The speed of sound is the by now familiar 343 m/s in
t
air at 20C. The time is 2.5 s, so…
This is again another basic v 
v
d
t
 d  v  t  343
m
 2.5 s  857.5 m
s
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 v  f problem.
v  f  440.0
cycles
m
 0.78 m  343.2
s
s
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 v  f problem with one complication. We need to recognize that the distance
between the center of a condensation and the center of an adjacent rarefaction of 65.23 cm
represents only ½.
v  f  256.0 Hz  2  0.6523 m   334.0
m
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 v  f problem where we need to solve for the wavelength  of the
sound.
v  f
m
v
s  0.457 m
  
f 750 Hz
343
The distance from one condensation to the next is one wavelength and is equal to 0.457 m or
m
m
m s
45.7 cm. (Note the units s  s    m )
1
Hz
s 1
s
15. The following sound waves have what velocity?
a. 20.0 Hz,  of 17.15 m
This is a straight forward v  f problem.
v  f  20.0 Hz 17.15m  343
m
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 10.0C?
This is a v 
d
problem where we first need to determine the speed of sound in air at 10C.
t
m

0.6 

m
m
m
m
v  331    s  10  C  331  6  337
s  C 
s
s
s




d
v
t
m
 d  v  t  337 10 s  3,370 m
s
The whistle blast travels a total distance of 3, 370 meters. Therefore the distance form the land
mass is ½ 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 v  f problem where we need to solve for the wavelength  of the
sound.
** SOLUTIONS Jaquin’s Sections **
SCI111 Homework Assignment #5
(20 Points Total)
v  f
ft
1,087
v
s  1.81 ft
 In air   
f 600 Hz
ft
4,920
v
s  8.20 ft
 In water   
f
600 Hz
The wavelength of this sound in the air is 1.81 feet and in the water is 8.20 feet.