Unit 1 Worksheet  Waves
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1. An oscillating block–spring system takes 0.75 s to begin repeating its motion.
Find (a) the period, (b) the frequency, and (c) the angular frequency.
2. In an electric shaver, the blade moves back and forth
over a distance of 2.0 mm in simple harmonic motion, with frequency
120
Hz.
Find (a) the amplitude, (b) the maximum blade
speed, and (c) the magnitude of the maximum blade acceleration.
3. An oscillator consists of a block attached to a spring
(k = 400 Nm^{1}). At some time t, the position (measured from the system’s equilibrium location), velocity, and acceleration of the
block are x = 0.100 m, v = 13.6 ms^{1}, and a = 123 ms^{2}.
Calculate
(a) the frequency
of oscillation,
(b) the mass of the block, and
(c) the amplitude of the motion.
4. A wooden block of mass M = 5.4 kg, at rest on a horizontal
frictionless table,
is attached to a rigid support by a spring of constant 6000 Nm^{1}. A bullet of mass m = 9.5 g and horizontal velocity, v, 630 ms^{1} strikes and is embedded in the block.
Assuming the compression of the spring is negligible until the
bullet is embedded, determine (a) the
velocity
of the system immediately after the collision and (b) the amplitude of the resulting simple harmonic motion.
5. A vertical spring stretches 9.6 cm when a 1.3 kg block is hung from its end. (a) Calculate the spring constant. This block is then displaced an additional 5.0 cm downward and released from rest. Find the (b) period, (c) frequency, (d) amplitude, and (e) maximum speed of the resulting SHM.
6. What is the frequency of a simple pendulum 2.0 m long
(a) in a room, (b) in an elevator accelerating upward at a rate of 2.0
ms^{2} and (c) in free fall?
7. A sinusoidal wave of frequency 500 Hz has a speed of
350 ms^{1}. (a) How far apart are two points that differ in phase by p/3
rad? (b) What is the phase difference between two displacements
at a certain point at times 1.00 ms apart?
8. A string ﬁxed at both ends is 8.40 m long and has a
mass of 0.120 kg. It is subjected to a tension of 96.0 N and set oscillating.
(a) What is the speed of the waves on the string? (b) What is the longest possible wavelength for a standing wave? (c) Give the frequency of that wave.
9. A nylon guitar string has a
linear density of 7.20 gm^{1} and is under
a tension of 150 N. The ﬁxed supports
are distance D, 90.0 cm apart. The
string is oscillating in a standing
wave pattern. Calculate the (a) speed, (b) wavelength,
and (c) frequency of the traveling waves whose superposition
gives this standing wave.
10. Earthquakes generate sound waves inside Earth.
Unlike a gas, Earth can experience both transverse (S) and longitudinal
(P) sound waves.
Typically, the speed of S waves is about 4.5
kms^{1}, and that of P waves 8.0 kms^{1}. A seismograph records P and S
waves from an earthquake. The ﬁrst P waves arrive 3.0 min before
the ﬁrst S waves. If the waves travel in a straight line, how far away did the earthquake occur?
11. Two
point sources S_{1} and S_{2} emit
sound of wavelength λ = 2.00 m.
The emissions are isotropic (the same intensity of radiation in all directions) and in
phase, and the separation between the sources, d is 16.0 m. At any
point P on the x axis, the wave fromS_{1} and the wave from S_{2 }interfere.
When P is very far away (x ≈ ∞),
what are (a) the phase difference
between the arriving waves from
S_{1} and S_{2} and (b) the type of interference they produce? Now
move point P along the x axis toward S_{1}. (c) Does the phase difference
between the waves increase or decrease? At
what distance x do the waves have a phase difference of (d) 0.50λ, (e)
1.00λ, and (f) 1.50λ?
12. A certain sound source is increased in sound
level by 30.0 dB. By what multiple is its intensity increased?
13. Suppose that the sound level of a conversation is initially at an angry 70 dB and then drops to a soothing 50 dB. Assuming that the frequency of the sound is 500 Hz, determine the (a) initial and (b) ﬁnal sound intensities.
14. (a) Find the speed of waves on a violin string of
mass 800 mg and length 22.0 cm if the fundamental frequency is
920 Hz. (b) What is the tension in the string? For the fundamental,
what is the wavelength of (c) the waves on the string and (d) the
sound waves emitted by the string?
15. The A string of a violin is a little too tightly stretched. Beats
at 4.00 per second are heard when the string is sounded together
with a tuning fork that is oscillating accurately at concert A (440
Hz).What is the (a) period of the violin string oscillation (b) frequency of the violin string oscillation?
16. A stationary motion detector sends sound waves of frequency 0.150 MHz and speed 343 ms^{1} toward a truck approaching at a speed of 45.0 ms^{1}. What is the frequency of the waves (a) detected by the truck, (b) reﬂected back to the detector?
