1. A pulse travels along a string with speed v. The tension of the string is FT and its linear mass density is
µ. At the peak of the pulse the shape of the string can be approximated as a circle of radius R. At the
peak consider a small segment of string of length ∆s > 0 subtended by a circle segment of angle ∆θ > 0.
The mass of the string segment and the magnitude of the restoring force are given respectively by:
A) Mass: µR∆θ; force: 2FT tan 21 ∆θ
B) Mass: µR∆θ; force: 2FT cos 21 ∆θ
C) Mass: µ−1 R∆θ; force: 2FT sin 12 ∆θ
D) Mass: µR∆θ; force: 2FT sin 12 ∆θ
E) Mass: µ∆s∆θ; force: 2FT sin 21 ∆θ
2. The speed of sound vi in a gas of density ρ with bulk modulus B is given by v =
of B and ρ are respectively
p
B/ρ. The dimensions
A) [B] = mass/(time length) and [ρ] = mass/length3
B) [B] = mass2 /(time2 length) and [ρ] = mass2 /length3
C) [B] = mass/(time3 length) and [ρ] = mass/(time length3 )
D) [B] = mass/(time2 length) and [ρ] = mass/length3
E) [B] = mass/(time2 length2 ) and [ρ] = mass/length4
3. A string of mass 0.0024 kg and length 0.70 m vibrates transversely in so that it contains half a wavelength
which vibrates at its fundamental frequency of 200. Hz. The tension on this string must be approximately
A)
82000. N
B)
540. N
C)
0.96 N
D)
270. N
E)
16. N
4. The speed of sound in dry air at 20.0 ◦ C is 343. m/ s. The speed of sound in dry air at 60.0 ◦ C is
A)
366. m/ s
B)
1030. m/ s
C)
322. m/ s
D)
594. m/ s
E)
390. m/ s
5. Which of the following functions does NOT describe a standing or propagating wave? A and c are
constants. The other symbols have their usual meaning.
A)
C)
E)
y(x, t) = Ap
sin(kx + ωt) B)
y(x, t) = A x − vt/c
D)
−vxt/c
y(x, t) = Ae
y(x, t) = 1/(x − vt)
y(x, t) = A cos kx sin ωt
Figure 1: Problem 6
6. As shown in Fig. 1, a wave is traveling with a speed v along the x axis in the positive direction. The upper
graph shows the displacement y versus the position x for a given instant of time. The lower graph shows
the displacement y versus the time t for any given point x. From the information in the graphs, what is
the wave speed v?
1
A) 8.0 m/ s
B) 6.0 m/ s
C) none of the other choices is correct
D) 4.0 m/ s
E) there is not enough information to solve the problem
7. A wave moving in the positive x direction has an amplitude of 0.4 m, a frequency of 0.25 Hz, and a
wavelength of 24 m. An equation, in which s and m are SI units, that describes this wave is
A)
B)
C)
D)
E)
y(x, t) = 0.4 m sin[2π(t/4 s + x/6 m)]
y(x, t) = 0.2 m sin[2π(t/4 s + x/24 m)]
y(x, t) = 0.2 m sin[0.5π(t/4 s − x/24 m)]
y(x, t) = 0.4 m sin[8π(t/ s − x/6m)]
y(x, t) = 0.4 m sin[2π(t/4 s − x/24 m)]
8. To double the rate at which energy is transmitted along a string, you could
A)
C)
E)
quadruple the tension in the string
double the amplitude of the wave
double the tension in the string
B) double the angular frequency of the source
D) halve the linear density of the string
9. The sound level of a dog’s bark is 50 dB. The intensity of a rock concert is 10,000 times that of the dog’s
bark. What is the sound level of the rock concert?
A)
90 dB
B)
500, 000 dB
C)
54 dB
D)
2000 dB
E)
10, 050 dB
Figure 2: Problem 10
10. As shown in Fig. 2, a pulse moves in a string toward a free end (a ring on a post) as indicated in the
sketch. On reflection, the pulse would most nearly be represented by
A)
4
B)
3
C)
1
D)
5
E)
2
11. While you are standing on a corner, a police car with a 2.00 kHz siren drives past you at 30 m/ s with its
siren on. The speed of sound is 340 m/ s. After the car has passed, the frequency you hear is about
A)
1800. Hz
B)
1770. Hz
C)
1840. Hz
D)
2190. Hz
E)
2180. Hz
12. The Mach angle of the shock wave produced by a jet traveling at Mach 3.0 at an altitude of 3000 m (assume
the speed of sound to be 340. m/ s at this altitude) is approximately
2
A)
16.◦
B)
18.◦
C)
21.◦
D)
23.◦
19.◦
E)
3