course Phy232
Assignment 14 Ch. 16 Problems: 47, 51, 54, 58, 6347.
(A): In a sinusoidal sound wave, the pressure variation given by Eq. (16.4) is greatest where the displacement given by Eq. (16.1) is zero.
Because that is the highest and lowest part on the waves. The compressions are rarefactions are points of zero displacement.
I cannot assess this problem from the information provided.
51. Playing a small flute 10.75cm long, open at one end and closed at the other, fundamental frequency of 600Hz. Speed of sound= 344.0m/s for which harmonics of flute will the string resonate? Which harmonic of string is in resonance?
The flutes harmonic 3N resonances with the string harmonic 4N
This seems plausible, but without string parameters (e.g., length, tension, mass) I can't tell
54.
(A) why are the ends antinodes and not nodes?
The fingers act as a pivot and the bar acts like a teeter-totter and proves that motion. It results from an elastic response to a disturbance. The greatest amount of amplitude is located at the ends which makes them the antinodes.
it's not exactly a teeter-totter motion, but the analogy isn't bad; the ends have opposite phases. From subsequent information provided it appears that the oscillation is logitudinal rather than transverse.
(B): Fundamental frequency can be obtained by stroking the rod while it is held the rod to obtain the fundamental.
When holding the rod any place but the center, this causes the wavelength to change making one end longer than the other. Since the fundamental frequency is in essence the smallest frequency corresponding to the largest wavelength which offsets L would produce on unappropriatley sized wavelength.
Right; for most positions this would result in destructive interference
(C): Calculate the fundamental frequency of a steel rod of L=1.50m
5941m/s divided by (2)(1.5m)= 1980.3 Hz f=v/2L
(D): What is the next possible standing wave frequency of this rod? Where should the rod be held to excite a standing wave of this freq.?
v/2L=5941/1.5 =3960.67Hz
The rod should be held on one end.
The rod must be held at an antinode; the ends are nodes and holding by an end would quickly dissipate all the energy.
The node-antinode configuration of the fundamental is ANA. The configuration for the next possible harmonic would be ANANA with the rod held at one of the N points. That would put the point 1/4 of the rod's length from an end.
58. Auditory canal extends 2.5cm from outside ear to eardrum
(A): explain why the human ear is especially sensitive to sounds at frequencies around 3500Hz. Use v=344 m/s
Because the pressure is so high that the ear is really sensitive to the sounds and will probably start making the ear hurt.
That's not it. What would be a resonant frequency for a tube of length 2.5 cm and open at one end?
(B): Yes, I would assume that the pressure would be so high that it would hurt the ear causing it to be sensitive to the sound.
This question is not specified in your document.
63. Wall has resonant frequency =600Hz. Car= c=3-m/s
(A): At what frequency must the soprano sing so the wall crumble?
548Hz
(B): 652 Hz
the question is unclear; assuming the soprano is in the moving car, the result should match the doppler frequency observed for a 600 Hz source moving at the speed of the car. Your results are plausible but you should show the details.