Problems
541
hears the sonic boom, followed 2.80 s later by the sound
of the rocket engine. What is the Mach number of the
aircraft?
62. A police car is traveling east at 40.0 m/s along a straight
road, overtaking a car ahead of it moving east at 30.0 m/s.
The police car has a malfunctioning siren that is stuck at
1 000 Hz. (a) Sketch the appearance of the wave fronts of
the sound produced by the siren. Show the wave fronts
both to the east and to the west of the police car. (b) What
would be the wavelength in air of the siren sound if the
police car were at rest? (c) What is the wavelength in
front of the police car? (d) What is it behind the police
car? (e) What is the frequency heard by the driver being
chased?
63. The speed of a one-dimensional compressional wave trav-
eling along a thin copper rod is 3.56 km/s. A copper bar is
given a sharp compressional blow at one end. The sound
of the blow, traveling through air at 0°C, reaches the oppo-
site end of the bar 6.40 ms later than the sound transmit-
ted through the metal of the bar. What is the length of
the bar?
64.
A jet flies toward higher altitude at a constant speed of
1 963 m/s in a direction making an angle 0 with the hori-
zontal (Fig. P17.64). An observer on the ground hears the
jet for the first time when it is directly overhead. Deter-
mine the value of 0 if the speed of sound in air is 340 m/s.
With particular experimental methods, it is possible to
produce and observe in a long thin rod both a longitudi-
nal wave and a transverse wave whose speed depends pri-
marily on tension in the rod. The speed of the longitudi-
nal wave is determined by the Young’s modulus and the
density of the material as
. The transverse wave can be
modeled as a wave in a stretched string. A particular metal
rod is 150 cm long and has a radius of 0.200 cm and a
mass of 50.9 g. Young’s modulus for the material is
6.80 & 10
10
N/m
2
. What must the tension in the rod be if
the ratio of the speed of longitudinal waves to the speed of
transverse waves is 8.00?
68.
A siren creates sound with a level - at a distance d from
the speaker. The siren is powered by a battery that delivers
a total energy E. Let e represent the efficiency of the siren.
(That is, e is equal to the output sound energy divided by
the supplied energy). Determine the total time the siren
can sound.
69.
The Doppler equation presented in the text is valid when
the motion between the observer and the source occurs on
a straight line, so that the source and observer are moving
either directly toward or directly away from each other. If
this restriction is relaxed, one must use the more general
Doppler equation
where 0
O
and 0
S
are defined in Figure P17.69a. (a) Show
that if the observer and source are moving away from each
other, the preceding equation reduces to Equation 17.13
with negative values for both v
O
and v
S
. (b) Use the pre-
ceding equation to solve the following problem. A train
moves at a constant speed of 25.0 m/s toward the intersec-
tion shown in Figure P17.69b. A car is stopped near the in-
tersection, 30.0 m from the tracks. If the train’s horn emits
a frequency of 500 Hz, what is the frequency heard by the
passengers in the car when the train is 40.0 m from the in-
tersection? Take the speed of sound to be 343 m/s.
f . #
!
v $ v
O
cos0
O
v * v
S
cos0
S
"
f
√Y/!
67.
θ
Figure P17.64
A meteoroid the size of a truck enters the earth’s atmos-
phere at a speed of 20.0 km/s and is not significantly
slowed before entering the ocean. (a) What is the Mach
angle of the shock wave from the meteoroid in the atmos-
phere? (Use 331 m/s as the sound speed.) (b) Assuming
that the meteoroid survives the impact with the ocean sur-
face, what is the (initial) Mach angle of the shock wave
that the meteoroid produces in the water? (Use the wave
speed for seawater given in Table 17.1.)
66. An interstate highway has been built through a poor
neighborhood in a city. In the afternoon, the sound level
in a rented room is 80.0 dB, as 100 cars pass outside the
window every minute. Late at night, when the tenant is
working in a factory, the traffic flow is only five cars per
minute. What is the average late-night sound level?
65.
f
S
v
S
f
O
v
O
(b)
25.0 m/s
(a)
θ
O
θ
θ
S
θ
Figure P17.69
70.
Equation 17.7 states that, at distance r away from a point
source with power !
av
, the wave intensity is
Study Figure 17.9 and prove that, at distance r straight
in front of a point source with power !
av
moving with
I #
!
av
4,r
2