Question

9. (a) A 1 m long string has a mass per unit length of 1.5×10−3 kg/m and is under a tension of 35 N. Find the first four harmonics of this string.

(b) A given pipe is 1.5 m long. If the speed of sound through this pipe is 343 m/s, what are the frequencies of the first three harmonics of the pipe when it is: (i) open at both ends, (ii) open at only one end.

10. A truck on a highway moves towards a police car sitting on the side of the highway. If the truck emits sound with a frequency of 1250 Hz as it moves, and an officer in the police car

detects a frequency of 1700 Hz for the sound, how fast is the truck moving?

Answer #1

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part 1. A 9.00-m long string sustains a three-loop standing wave
pattern as shown. The string has a mass of 45 g and under a tension
of 50 N.
a. What is the frequency of vibration?
b. At the same frequency, you wish to see four loops, what
tension you need to use.
Part 2.
a. Determine the shortest length of pipe, open at both ends,
which will resonate at 256 Hz (so the first harmonics is 256Hz).
The speed...

A string with a mass density of 3.6 ? 10-3 kg/m is
under a tension of 370 N and is fixed at both ends. One of its
resonance frequencies is 720 Hz. The next higher resonance
frequency is 840 Hz.
(a) What is the fundamental frequency of this string?
______Hz
(b) Which harmonics have the given frequencies? (Enter 1 for the
first harmonic, 2 for the second harmonic, etc.)
720 Hz
840 Hz
(c) What is the length of the...

A transverse wave propagates in a very long wire of mass per
unit length 4*10^-3 kg/m and under tension of 360 N. An observer
next to the wire notices 10 wave peaks (or crests) passing her in a
time of 2 seconds moving to the left.
a) If at t=0 and x=0 the displacement assumes its maximum value
of 1mm, what is the explicit equation for the wave?
b) Calculate the maximum longitudinal velocity for an
infinitesimal segment of the...

A string with a mass per length of 2.00 gm/m is stretched with a
force of 120 N between two points that are 0.400 m apart. The
fundamental frequency of the stretched string is in tune with the
frequency of the second mode of an organ pipe filled with air and
open at both ends. The velocity of sound in air at 0°C
is 331 m/s. If the temperature of the air decreases by
20°C, then what is the length...

A Piano that has a string of L = 2(m) long and a mass of m =
0.2(g) over that length. The Piano is tightened and its tension is
T = 20(N). Determine the speed of propagation for a wave along that
string? Let the fundamental mode has a wavelength of λ = L 2
Determine the frequency of sound associated with that string?

A stretched string is 1.91 m long and has a mass of 20.9 g. When
the string oscillates at 440 Hz , which is the frequency of the
standard A pitch, transverse waves with a wavelength of 16.7 cm
travel along the string. Calculate the tension ? in the string.

1.The human ear canal is about 2.3 cm long. If it is regarded as
a tube open at one end and closed at the eardrum, what is the
fundamental frequency around which we would expect hearing to be
most sensitive?
?kHz
2. An airplane traveling at half the speed of sound emits a
sound of frequency 5.30 kHz.
(a) At what frequency does a stationary listener hear the sound
as the plane approaches?
? kHz
(b) At what frequency does...

1. A cord of mass 0.65 kg is stretched between two supports 8.0
m apart. If the tension in the cord is 140 N, how long will it take
a pulse to travel from one support to the other?
2. A 50.0 Kg ball hangs from a steel wire 1.00 mm in diameter
and 6.00 m long. What would be the speed of a wave in the steel
wire?
3. The intensity of an earthquake wave passing through the earth...

A stone is dropped from the top of a cliff. The splash it makes
when striking the water below is heard 3.2 s later. How high is the
cliff?
2. The pressure variation is a sound wave is given by Δ P =
0.0035 sin (0.38 π x – 1350 π t) Determine a. the wavelength b. the
frequency c. the speed and d. the displacement amplitude of the
wave. Assume the density of the medium to be 2.2 x...

11. A simple pendulum undergoes small-angle oscillations. Which
of the following pairs (mass, string length) will oscillate with a
period greater than 2.2 seconds?
a) (0.50 kg, 1.0 m)
b) (0.40 kg, 0.80 m)
c) (1.0 kg, 0.50 m)
d) (0.80 kg, 0.40 m)
e) none of the above answers are correct
(numbers 15-17) An ideal horizontal spring-mass system begins
oscillation with the mass at x=0 (the spring is relaxed) and moving
in the -x direction at 6.00 m/s. The...

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