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Physics 1 Homework #5
Due: May 27
1. In the figure, two identical springs of spring constant 7580 N/m are attached to a block
of mass 0.245 kg. What is the frequency of oscillation on the frictionless floor?
2. A nylon guitar string has a density of 7.20 g/m and is a tension of 150 N. The fixed
supports are distance D = 90.0 cm apart. The string is oscillating in the standing wave
pattern shown in the figure. Calculate the (a) speed, (b) wavelength, and (c) frequency of
the traveling waves whose superposition gives this standing wave
3. The figure shows two isotropic point sources of sound, S1 and S2. The sources emit
waves in phase at wavelength 0.50 m; they are separated by D = 1.75 m. If we move a
sound detector along a large circle centered at the midpoint between the sources, at how
many points do waves arrive at the detector (a) exactly in phase and (b) exactly out of
phase?
4. Let’s consider the particle of mass m and charge e which is bounded to the spring. We
can assume this particle as a damped simple harmonic oscillator. When the electric field is
present, this oscillating particle radiates an electromagnetic wave. Determine the
displacement of the particle from its equilibrium position. You may use damping constant
b and spring constant k.
5. You learned one dimensional wave equation in chapter 16. (a) Derive the one
dimensional wave equation. (b) Obtain the two dimensional wave equation and the three
dimensional wave equation.
6. (a) Derive the Doppler effect equation when the detector is moving and the source is
stationary. (b) Derive the Doppler effect equation when the source is moving and the
detector is stationary. (c) Derive the general Doppler effect equation. You may assume that
detector and source are both moving.
7. A simple pendulum is attached to a wagon. Length of the pendulum is L. The wagon
slides down a slope without friction. The angle between the slope and the horizontal is θ.
Evaluate the period of the pendulum.
8. In the figure below, an aluminum wire of length L1 = 60.0 cm, cross-sectional area
1.00
10-2 cm2, and density 2.60 g/cm3, is joined to a steel wire of density 7.80 g/cm3 and
the same cross-sectional area. The compound wire, loaded with a block of mass m = 10.0
kg, is arranged so that the distance L2 from the joint to the supporting pulley is 86.6 cm.
Transverse waves are set up in the wire by using an external source of variable frequency;
a node is located at the pulley. (a) Find the lowest frequency that generates a standing
wave having the joint as one of the nodes. (b) How many nodes are observed at this
frequency?
9. Figure shows two point sources S1 and S2 that emit sound of wavelength λ = 1.64 m.
The emissions are isotropic and in phase, and the separation between the sources is d =
16.4 m. At any point P on the x axis, the wave from S1 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 S1 and S2 and (b) the type of interference they produce? Now move point P
along the x axis toward S1. (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?
10. A sperm whale vocalizes by producing a series of clicks. Actually, the whale makes only
a single sound near the front of its head to start the series. Part of that sound then emerges
from the head into the water to become the first click of the series. The rest of the sound
travels backward through the spermaceti sac (a body of fat), reflects from the frontal sac
(an air layer), and then travels forward through the spermaceti sac. When it reaches the
distal sac (another air layer) at the front of the head, some of the sound escapes into the
water to form the second click, and the rest is sent back through the spermaceti sac (and
ends up forming later clicks). The Figure shows a strip-chart recording of a series of clicks.
A unit time interval of 1.0 ms is indicated on the chart. Assuming that the speed of sound
in the spermaceti sac is 1372 m/s, find the length of the spermaceti sac. From such a
calculation, marine scientists estimate the length of a whale from its click series.