PHY2464 Exam 1 – Hall, Ch 1-5    092707

 

SOLUTIONS

 

If you don't follow the somewhat abbreviated solutions given here, please ASK!

 

Useful (?) constants:   g = 9.8 m/s2       Io = 10-12 W/m2     k='kilo' = 103       M='mega' = 106

 G='giga'= 109    speed of sound in air at 20oC = 344 m/s   1 atm pressure = 105 N/m2  = 14.7 lb/in2

[For this exam, you may assume that SIL = SPL]

Part I.  Multiple-choice questions (5 points each):  print the letter designating the answer of your choice in the blank to the left of the question.

 

__A__1. The pressure amplitude of sound waves at comfortable listening levels averages about

 0.1 N/m2, which is approximately

 

            A.  10-6 atm      B. 0.001 atm       C. 0.1 atm      D. 1 lb/in2     E. none of these 

 

__D__2. The frequency of a sound wave is the reciprocal of its

 

            A. dispersion      B. wavelength     C. amplitude      D. period     E.  none of these

 

__B__3.  Chapter 3 emphasized that sound sources always ______ and that producing or

 causing this action requires ______.

 

A. are visible; intensity     B.  vibrate; energy    C.  produce steady tones; no work   

D.  must be struck;  no force     E.  none of these

 

__E__4.  Beat notes (or frequencies) are good examples of what wave  phenomenon?

 

A. diffraction     B. none of these   C.  absorption    D. refraction    E. interference

 

__D__5. We've learned that  temperature variations produce changes in which of the following

parameters of a sound:      (1) frequency,  (2) wavelength,  (3) speed       ?

 

            A. (1) and (2) only     B.  (1), (2), and (3)    C. (2) and (3) only  D. (1) and (3) only

            E. (3) only

See Quiz 1.....since the initiating vibrations don't change, only frequency and speed are affected!

 

__C or E__6.  The 'comfortable listening level' [referred to in question 1] of . 0.1 N/m2 pressure

amplitude corresponds to what sound intensity level in dB ?

 

                    A.  100    B.  50    C. none of these    D. 60     E. 70

SPL = 20 log I/I0 where I0 = 2x10-5 N/m2   

This gives 74.4 dB, so either '70' or 'none' is acceptable.

 

 

__B__7. Sound waves are not

A. refractable     B.  transverse    C.  reflectable    D. refrangible      E.  diffractable

"Refrangible' means 'refraactable'!!

 

__E_9.  The speed of radio waves (and all electromagnetic waves, including light) is about

            3 x 108 m/s.  From what you've learned about diffraction, which of the following wave

categories would  you expect to be most affected (interrupted, blocked or scattered) by

buildings, trees, and other obstacles between you and the sending antenna(s)?

 

            A. AM radio (1000kHz)   B. FM (100MHz)     C. long wave radio (100 kHz)   

D.  TV (500 MHz)    E.  cellular telephone (0.9 GHz)

 

__A__10.  I stand half way between two loudspeakers, with one on my left and one on my right. 

 A musical note from the speakers gives me constructive interference. How far to my left

should I move to obtain destructive interference?

A. one-fourth of a wavelength    B. one-half of a wavelength    C. one wavelength

D. 1.10 wavelengths    E. none of these

 

Part II. For these questions, to obtain full credit please  (i) show your work (calculations) in the space provided; (ii) circle your final answer which (iii) must include proper units . Weighting is given in (parentheses). For more space, use the back of the page, clearly indicating that you did so.

 

11. (a) (5) The measured SIL of the sound from a loudly-played trombone is 84 dB at a location 3m away.  Calculate the intensity level for 4 similarly-played trombones at the same distance.

 

4 trombones => 4 X Intensity.  We know that each doubling of I  increases the SIL by 3 dB, so 4 trombones => 2 X 3 dB = 6 dB increase, or 84 dB + 6 dB = 90 dB

 

 

(b). (5) What is the intensity of one trombone's sound at this distance?

 

84 dB = 10 log I/Io => 8.4 = log I/Io , or I/Io = 108.4 =  2.5 x 106

 

Thus I/Io  =I/(10-12 W/m2) = 2.5 x 106  => I =  2.5 x 106  x 10-12 W/m2

= 2.5 x 10-4 W/m2

 

 

(c) (5) What is the acoustic power output of one of these trombones, assuming uniform distribution of the sound waves?

 

At 3 m distance, the sound waves spread over a spherical area of 3 m radius. 

The area S = 4pr2 =  4p (3m)2 = 113 m2

 

I = P/S  => P = IS  = 2.5 x 10-4 W/m2  x  113 m2 = 2.8 x 10-2 W [ or 28 mw]

 

 

 

12. (a) (5)Tripling the power output from a loudspeaker emitting a single frequency will result in

what increase in SIL?

 

Since I = P/S, tripling the power also triples I.

Thus I3/I1 = 3,  or I3 = 3I1

 

The SIL for I3 with respect to I1 is 10 log I3/I1 = = 10 log 3 = 10 (0.477) = 4.77

 

So the increase in SIL is 4.77 dB or close to 5 dB

 

[Note that you can also get this from Table 5.1]

 

 

 

 

 

12 (b) (5)Tripling the distance between sound source and  listener will change the intensity, as

detected by the listener, by what factor?

 

Triple distance = 3 x (radius).  

I = P/S where S = area over which the waves are spreading (assumed spherical)

S is thus proportional to r2 .

Thus tripled r = 3r  so area increases by (3r)2 =  9

 

Therefore I/I'  = S'/S   => I' = I (S/S') = I (1/9)

 => I is diiminished by a factor of 9

 

(c) (5) By how much does the amplitude of the waves change if the source-to-listener distance is tripled?

 

I is proportional to A2 so  I/I' = (A/A')2  

=> A/A' = …(I/I')

Thus A' = A {…(I/[I'/9]) = A …(1/9)  = A (1/3)  = A/3  i.e., A is reduced by a factor of 3

 

 

 

13. (a)(5) A currently-available 'ear-muff' hearing protector claims a noise reduction rating of 25 dB and that it may be safely used "at noise levels up to 98 dB".   What, then, is the ratio of sound intensity reaching the user's eardrums, compared with a 98 dB SIL outside of the ear muffs?

 

The SIL difference between outside and inside the earmuff is 25 dB, i. e.,

SILoutside - SILinside  = 25 dB

 

so 25 = 10 log Iout/Iin => log Iout/Iin = 2.5, or Iout/Iin = 102.5 = 316

 

 

 

(b) (5)  What percentage of the sound energy is being blocked out by the protector?

 

Since the ratio is 316, the fraction transmitted through the protector is 1/316.

Thus the fraction blocked is 1 - 1/316 0r 315/316 = 0.9968

 so the percentage blocked is 99.68%

 

 

 

 

14. (a) (5) The Gator Band is invited to provide half-time entertainment on the field at a brand-new bowl game, the 'Ice Bowl', to be played in North Dakota in mid-December.  The temperature on the field is 14o F  (-10o C ).  In this venue, what is the speed of sound ?

 

v = 344m/s + 0.6 (T - 20oC)

T is -10 oC,  so [-10 -20] = -30

 

Thus v = 344 + 0.6 (-30)  = (344 - 18) m/s  = 326 m/s

 

 

 

(b) (5) If the brass playersŐ instruments were last tuned on Florida Field (20o C), what would be the frequency of a played 'middle C'  [261 Hz] in the Ice Bowl?

 

v =f l  => f = v/l     so we can write    f'/f =  v'/v

 

Thus f' = f (v'/v) =  261 Hz (326/344) = 247 Hz