Chapter SOUND WAVES Intrductin: A sund wave (r pressure r cmpressin wave) results when a surface (layer f mlecules) mves back and frth in a medium prducing a sequence f cmpressins C and rarefactins R. Althugh individual mlecules d nt travel any appreciable distance, the disturbance travels utwards. The cmpressin is a regin where the mlecules f the medium are very clse t each ther and the pressure is higher than nrmal pressure. The rarefactin is a regin where the mlecules are farther away frm each ther and the pressure is lwer than the nrmal pressure Sund prpagates in the frm f lngitudinal waves thrugh a medium. In such a wave, the particles f the disturbed medium mve parallel t the wave velcity. The sund waves have the fllwing categries: i. Audible sund has a frequency frm 0 Hz t 0,000 Hz. ii. Infrasnic are the frequencies lwer than 0 Hz, and iii. ultrasnic are frequencies higher than 0,000 Hz. Sund waves have the fllwing prperties: 1. They can travel thrugh slids, liquids r gasses, but nt vacuum.. The speed f sund is a cnstant fr a given material at a given pressure and temperature. Fr example, the speed f sund in air, v, at 1 atmspheric pressure and 0 C is equal t 331 m/s. 3. Speed f sund in air ( air v ) < speed f sund in liquid ( liquid v ) < speed f sund in slid ( slid v ). This is mainly related t the intermlecular spaces in a substances. 1
4. When sund ges frm lw dense medium (e.g. air) int a higher dense medium (e.g. liquid) the frequency stays unchanged, the velcity increases, and thus the wavelength must increases, recall the relatin v f. 5. Speed f sund increases with increasing the temperature. Recall the empirical frmulae: v v + 0.6 T, T is in C where v = 331 m/s. T T vt v, T is in Kelvin 73 Calculate the speed f sund at 7 C, using tw different methds. v7 v + 0.6 T 3310.67 347 m/s. v7 73 7 331 347 m/s. 73 6. Speed f sund in different media is expressed as: Y N v(slids), Y is the Yung's mdulus, [ Y]= Pa m B N v(liquids r gases), B is the Bulk's mdulus, [ B]= Pa m P The Bulk s mdulus is defined as B, where V / V is the fractinal change in the V / V vlume prduced by a change in the pressure P. B fr liquid is mre than 10 3 times greater than that f air, this is why v v. liquid air Assuming the velcity f sund in air at 0 C is v = 331 m/s, calculate the change in the wavelength due t a frequency f f = 1000 Hz when the temperature changes frm 0 C t 30 C. At 0 v 331 C, 0.331 m., f 1000 At 30 v 30 303 C, T = 303 K, then 30 0.349 m., f 73 and the change in the wavelength is 30 0.018 m = 18 mm A man strikes a lng steel rd at ne end. Anther man, at the ther end with his ear clse t the rd, hears the sund f the blw twice (nce thrugh air and nce thrugh the rd), with
time interval t = 0.1 s between them. Hw lng l is the rd? [Fr the steel, Y =.1x10 11 Pa, and the = 7.0x10 3 kg/m 3. Speed f sund in air v = 340 m/s.] The speed f sund in the steel is v then 11 Y.110 5477 m/s, 3 7.010 l l vv t l t, v v v v 5477340 l 0.1 36 m. 5477 340 Harmnic sund waves: The harmnic displacement alng x-directin, S( x, t ), is given by: Sxt (, ) Sm cs( kx- t) where S m is the maximum displacement (amplitude). The change in pressure, Pxt (, ), f the lngitudinal wave frm its equilibrium value is given by: Pxt (, ) Psin( kx- t), where is the maximum amplitude and has the frm: Pm ρ is the vlume density The average energy: ( E m m P vs m mass ( ). Nte that Sxt (, ) and ΔP(x,t) are ut f phase by 90. Vlume average, [E] = J), the average energy f the mving layer, with thickness x and area A, f the lngitudinal wave is: 1 1 Eaverage m( Sm) A ( A x)( Sm) where A x is the vlume f the layer. The average pwer: ( P by E average t, [P] = W), transmitted in a harmnic sund wave is defined 1 P v( Sm) A x where v wave speed. t The intensity: (I = P A, [I]= W ( )), is the energy per secnd m flwing nrmally thrugh an area f 1 m at the place cncerned. Fr sund wave, it is defined as (Pwer/Area) 1 P m I v( Sm) v r I1 I 3 r 1
Because the sund waves spread ut as they mve away frm their surce, their intensity decreases with distance and beys the inverse-square law, i.e. I 1/r. The fllwing rati is als useful: I1 r ( ) I r 1 Spherical waves: At a distance r frm spherical (pint) surce, the ttal pwer is distributed ver the 4 r area f a sphere f radius r. Hence the intensity f the sund at this distance is: P I. 4 r A pint surce f sund wave has average pwer f 1.00 10 ⁶ W. What is the intensity 3.00 m away frm the surce? 6 P 1.0010 I 8.8410 W/m 4r 4 3 9 Assume that sund frm a plane engine enters yur ear nrmally with intensity f 0.05 W/m². If yur ear passage has a crss-sectinal area f 38 mm², hw many Jules f energy per secnd enter yur ear? 6 6 P IA (0.05)(38 10 ) 1.9 10 J/s. Sund level: (β, [β] = db Decibel), is defined by: where I /10 10lg10 I I 10, I 1 W I 10 is the lwest audible sund (the threshld f hearing). m Find the rati f the intensities f tw sund waves if the difference in their sund levels is 7 db. I I I 10lg( ) 10lg( ) 10lg( ) 7 db 1 1 I I I1 This gives the rati: I I 7/10 10 5. 1 4
The sund level m frm a surce is measured t be 90 db. Hw far away must ne be t measure a sund level f 50 db? 90 db I I 10 10 W, m 50 db I I 10 10 W, 90/10 3 1 1 50/10 7 I r I 10 ( ) 00 m. I I 10-3 1 1 r r1-7 r1 m Interference f sund waves: The path length difference, r, in case f interference between tw traveling waves, is related t the phase difference,, by the relatin: r r r1 in phase (fully cnstructive) ut f phase (fully distructive) r n, n is even r n, n is dd A listener hears tw sund waves frm tw lud-speakers, with the same frequency f 85 Hz that are in phase. At the listener s lcatin a phase difference f 450 is detected. What is the path difference if the speed f the waves is 340 m/s. 450 340 180 r ( )( ) 5 m. 85 A sund wave f wavelength λ = 50.0 cm enters the tube shwn in figure (1) at the surce end. What must be the smallest radius r, ther than zer, such that a maximum sund will be heard at the detectr end? Surce r Figure (1) Detectr 5
In this case, use n = in the fully cnstructive interference r L r ( ) r r 0.44 m L n, we can get: Hmewrk: What must be the smallest radius r, ther than zer, such that a minimum will be detected at the detectr end?. Tw speakers, A and B, are driven by a cmmn scillatr A 1.75 B at 700 Hz and face each ther at a distance f 1.75 m Lcate the pints alng a line jining the tw speakers. Where x relative minima (ndes) wuld be expected. [Use: v = 350 m/s] Suppse that the distance x frm the speaker A, then r x, r 1.75x 1 r r r 1.75 x 1. Fr the minimum, equate r n, n is dd, where 1.75 0.5n ne can find: x S, there are 6 minima between the tw speakers. Neglect the minima at the speakers psitin 350 0.5 m, then slving fr x, 700 n x r 1.75 x -7 1.75 0.0-5 1.5 0.5-3 1.5 0. 5-1 1.00 0.75 1 0.75 1.00 3 0.5 1.5 5 0.5 1.50 7 0 1.75 6
Resnances in air clumns: Standing waves are examples fr lngitudinal waves where ndes are frmed at the clsed ends and antindes at pen ends (always). Resnance means reinfrcement f sund; by means, when the frequency f the vibrating surce is equal t the frequency f the vibratins f the air clumn. In case f resnance, the relatin between the frequency (fn), speed f sund (v), and the length f the tube (L) is defined by: v nf 1, f 1, n 1,,3, (fr pen-pen tube) f n L v nf 1, f 1, n 1,3,5, (fr pen-clsed tube) 4L n takes the values: 1 fr the fundamental (first harmnic),, fr the secnd harmnic, 3 fr the third harmnic, etc. Ntice that: 1- In an pen-pen tube, all the harmnics are allwed and the number f ndes is less than the number f antindes. - In an pen-clsed tube, nly the dd harmnics are allwed and the number f ndes is equal t the number f antindes. 7
An air clumn m in length is pen at bth ends. The frequency f a certain harmnic is 410 Hz, and the frequency f the next higher harmnic is 49 Hz. Determine the speed f sund in the air clumn. Suppse that fn nf1 410 Hz, and fn 1 ( n1) f1 49 Hz By subtractin ne gets: f1 fn 1 fn 8 Hz, and this gives: v L( f1) 8 38 m/s. als f 410 n n 5. f1 8 If tw adjacent natural frequencies f an rgan pipe (pen at ne end) are determined t be is 550 Hz and 650 Hz, calculate the fundamental frequency and the length f this pipe. (Speed f sund in air 340 m/s) Assuming that the resnances ccur at n and n +, then f nf 550 Hz, and f ( n) f 650 Hz n 1 n 1 Dividing the tw equatins ne gets: 8
n 550 n 650 n 11 S, the fundamental frequency is f1 550 /11 50 Hz. T calculate the length, we knw that the resnance in a tube pen at ne end, the frequency is given by the relatin and the wavelength is: v 340 340 f n ( n) L 1.7 m. 4L 4 f 450 4L 6.8 m. A tube f length L = 1.5 m is clsed at ne l,m end. A stretched wire is placed near the pen end, see figure. The wire has a length l = 0.5 m and mass f m = 7.5 g. It is fixed at bth ends and vibrates in its fundamental mde. By resnance, it sets the L air clumn in the tube int scillatin at that clumn s fundamental frequency. Find the tensin in the wire. [Speed f sund in air v = 340 m/s.] 1 v 1 F Fr the wire f1, and fr the tube. f1 l l finds: v 4L. By equating bth equatins ne F 3 v l 7.510 (340) (0.5) ( ) 4 N. 4L 0.5 4 (1.5) Dppler Effect: the relatin between the frequency emitted by a surce, f s, and the frequency heard by an bservable, f, is given by: f v v fs v vs 9
where v is the speed f sund in air. The subscripts and s are used t represent the bserver and the surce respectively. Upper signs are used when the surce and the bserver mve tward (apprach) each ther. Lwer signs are used when the surce and the bserver mve away frm each ther. A passenger in an autmbile is traveling at m/s tward a statinary siren that is emitting a 0 Hz nte. Calculate the frequency that the passenger hears. The speed f sund in air is 345 m/s. f 345 0 34 Hz, 345 A sund wave is incident upn a racing car mving tward the surce with speed f 0.5 v, where v is the speed prpagatin f sund wave. The sund wave frequency measured in the car is 1.0 10⁶ Hz. What is the frequency f the surce? v 0.5v v 6 6 f fs fs 1.0 10 Hz =0.8 10 Hz, Standing at a crsswalk, yu hear a frequency f (appraching) =550 Hz frm a siren n an appraching plice car. After the plice car pass, the bserved frequency f the siren is f (away) =410 Hz. Determine the car's speeds v s frm the bservatins. (Speed f sund in air = 343 m/s.) then f 343 (appraching) f s 550, 343v s f 343 (away) f s 410, 343v s 10
550 343 v s v s 50 m/s. 410 343 v s A plice car mving at 0 m/s with its hrn blwing, at frequency f f s =100 Hz, is chasing anther car ging at 16 m/s. What is the apparent frequency f the hrn as heard by the driver being chased? Take the speed f sund in air t be 340 m/s. f 340 16 (chasing car) 100 115 Hz. 340 0 Tw cars are heading straight at each ther with the same speed vc. The hrn f ne, with frequency f 3000 Hz, is blwing, and is heard t have a frequency f 3300 Hz by the s peple in the ther car. Find vc if the speed f sund is 340 m/s. 340 v c 3300 3000 v c 16. m/s. 340 v c The whistle n a train generates a tne f 440 Hz as the train appraches a statin at 30 m/s. (assume the speed f sund in air = 331 m/s.) (a) Find the frequency that a statinary bserver standing at the statin will hear. f 331 0 440 484 Hz, 331 30 (b) Suppse a wind blws at 0 m/s in the same directin as the mtin f the train. What is the frequency that a statinary bserver standing at the statin will hear? f 331 0 440 481 Hz, 3310 30 T determine the speed f a mving car v c, a sund f frequency f s = 500 Hz is sent frm a statinary plice car. The sund is reflected back the car and detected by the plice car with a new frequency f ' s = 600 Hz. 11
(a) Write dwn an expressin fr the frequency f c detected by the driver f the car. f v v v c c fs (c) Calculate the speed f the car. (Speed f sund in air v = 333 m/s). v v v c f ' s f c f s v vc v vc 600 333v c v c 30.3 m/s. 500 333v c (c) If the speed limit is 90 km/h, des the driver f the car deserve a speed ticket? v c 30.3 m/s 109 km/hurs The driver deserves a speed ticket. 1
True and False Statements 1. Mechanical waves need a medium t prpagate. T. Sund is a frm f energy. T 3. Sund waves are transverse waves. F 4. Sund is a lngitudinal wave prduced by vibrating surce. T 5. Sund needs a medium t prpagate thrugh. T 6. The speed f sund depends n the density f the medium. T 7. The speed f sund increases with increasing the temperature the medium. T 8. Sund travels in air as cncentric waves f cmpressin and rarefactin. T 9. A sund wave travels frm air t water, then its speed increases. T 10. A sund wave travels frm air t water, then its frequency decreases. F 11. Fr a tube clsed at ne end, nly dd harmnics are present. T 1. Fr a tube pen at bth ends, nly dd harmnics are present. F 13. Fr a tube pen at bth ends, number f ndes = number f antindes. F 14. Fr a tube clsed at ne end, number f ndes < number f antindes. F 15. The speed f sund increases with increasing the temperature f. T nv 16. The frmula f n, (n = 1,3,...) is used fr a tube pen at bth ends. F 4L 13
Supplementary Prblems When a sund wave travels frm air int steel, (a) it changes frm a lngitudinal wave int transverse wave. (b) it's velcity decreases. (c) it's frequency increases. (d)@ it's wavelength increases. (e) it becmes mre intense. A man strikes a lng steel rd at ne end. Anther man, at the ther end with his ear clse t the rd, hears the sund f the blw twice (ne thrugh air and nce thrugh the rd), with a 0.1 secnds interval between. Hw lng is the rd? [Fr the steel, the bulk mdulus =.1 10 11 Pa, and the = 7.0 10 3 kg/ m 3. Speed f sund in air = 340 m/s.] (a) 4 m. (b) 34 m. (c)@ 36 m. (d) 40 m. (e) 44 m. Sund waves (a) are matter waves. (b) travel at the same speed in all media. (c)@ are mechanical waves. (d) are transverse waves. (e) are electrmagnetic waves. Sund waves are nt: (a) pressure waves. (b) mechanical waves. (c) cmpressin waves. (d)@ transverse waves. (e) lngitudinal waves. In the figure, the tw bservers at A and B are hearing the sund emitted by the pint surce S. What is the time difference between hearing the sund at the tw lcatins? Use 345 m/s as the speed f sund. (a) 3.17 s 14
(b) 0.053 s (c)@ 0.315 s (d) 0.368 s (e) 1.89 s The vlume f a certain slid shrinks by parts in 10 6 when it is subject t an external hydrstatic pressure f 1 atm. f the slid is 8.0 g/cm 3. What is the speed f a lngitudinal wave thrugh this material? (a) 3.4 10 3 m/s. (b) 1.5 10 3 m/s. (c).5 10 m/s. (d)@.5 10 3 m/s. (e) 3.4 10 m/s. In a liquid having =1.30 10 3 kg/ m 3, lngitudinal waves with frequency f 400 Hz are fund t have a wavelength f 8.0 m. Calculate the bulk mdulus f the liquid. (a) 6.64 10 1 Pa. (b)@ 1.33 10 10 Pa. (c) 9.6 10 7 Pa. (d) 3.1 10 6 Pa. (e) 1.0 10 11 Pa. B Hint : v B v ( f ) B 3 10 1.30 10 (400 8) 1.33 10 Pa 15
If tw sund waves, ne in air and the ther in water, are f equal intensity. What is the rati f the pressure amplitude f the wave in water t that f the wave in air? ( (air)= 1.1 kg/m 3, v(air)= 343 m/s, (water)= 1 10 3 kg/m 3, v(water)= 148 m/s) (a) 78. (b) 35.7 (c) 99. (d) 8.3 (e)@ 59.8 The maximum pressure amplitude that the human ear can tlerate in lud sunds is 8 Pa. What is the displacement amplitude fr such a sund in air f = 1.1 kg/m 3 at a frequency f 5.0 10 3 Hz? [speed f sund in air = 343 m/s]. (a) 4.15 10-6 m. (b) 50.5 10-6 m. (c) 11.0 10-6 m. (d)@.15 10-6 m. (e) 8.30 10-6 m. A sinusidal sund wave is described by the displacement S (x,t) = 10-8 cs [1.5 x - 1850 t], where x is in meters and t is secnds. What is the pressure amplitude f this wave if it is traveling in a material with a bulk mdulus f.1 10 9 N/ m? (a)@ 53 Pa (b) 77 Pa (c) 66 Pa (d) 8 Pa (e) 44 Pa 16
Tw identical speakers, facing each ther are driven by a cmmn scillatr f frequency 600 Hz. A man, at the midpint between the speakers, starts mving tward ne f them. He reaches the first minimum sund when he is 1 m frm ne f the speakers. Find the distance between the speakers. (Speed f sund = 343 m/s.) (a) 6.1 m (b) 4.0 m (c)@.3 m (d) 5.6 m (e) 4.5 m Tw speakers are driven by a cmmn scillatr and face each ther at a distance f 1.500 m. A man is standing at 0.700 m frm ne f the speakers alng the line jining the tw speakers. What is the highest frequency f the scillatr, within the audible range (0.0 Hz t 0.0 khz), s that the man hears a minimum sund? (Speed f sund = 343 m/s). (a) 19.9 khz (b)@ 18.9 khz (c) 1.6 khz (d) 15.9 khz (e) 10.3 khz Tw sund waves, frm tw different surces with the same frequency, 660 Hz, travel at a speed f 330 m/s. The surces are in phase. What is the phase difference f the waves at a pint that is 5.0 m frm ne surce and 4.0 m frm the ther? (The waves are traveling in the same directin.) (a) 1. (b). (c)@ 4. (d) 3. (e) 5. 17
A sund wave f 50.0 cm wavelength enters the tube shwn in figure(1) at the surce end. What must be the smallest radius(r) (ther than zer) such that a maximum sund will be heard at the detectr end? (a) 15.9 cm. (b) 1.3 cm. (c) 33.0 cm. (d) 17.5 cm. (e)@ 43.8 cm. Tw pint surces S1 and S are placed n the y-axis as shwn in figure 1. The tw surces are in phase and emit identical sund waves with frequency 860 Hz. An bserver starts at pint A and mves t pint B alng a straight line parallel t the y-axis. Hw many pints f maximum intensity (cnstructive interference) will he bserve? (speed f sund in air = 344 m/s). (a) 1 (b) 4 (c) 0 (d)@ 5 (e) 3 At the mid-pint between A and B: r 0 maximum At the starting pint A r B: r 5 4 1 m v 344 Cmpare with: r n n( ) n n0. f 860 1 ne finds n 5 0. S, he will statr at A with ( n 5) i.e. minimum, and will g t thrugh the maximum with n 4,,0,,4. Tw small identical speakers are in phase(see figure ). The speakers are 3.0 m apart. An bserver stands at pint X, 4.0 m in frnt f ne f the speakers. The sund he hears will be a maximum if the wavelength is 18
(a).0 m. (b) 3.0 m. (c) 1.5 m. (d)@ 1.0 m. (e).5 m. Tw speakers face each ther and emit sund waves in air with a frequency f 500 Hz, as shwn in figure 1. The phase difference between the sund waves emitted by the tw speakers at pint A is.35 radians. What is the distance between A and S? The speed f sund in air is 343 m/s. (a) 0.56 m (b) 1.05 m (c) 3.17 m (d)@ 0.756 m (e) 0.500 m Tw identical speakers A and B are driven by a cmmn scillatr at 56 Hz and face each ther at a distance f 10.0 m (see figure ). A small detectr is lcated midway between the tw speakers (at pint O). Find the distance that the detectr has t mve twards A alng the line jining A and B t detect the first minimum in the sund intensity. [speed f sund in air = 343 m/s]. (a) (b) 0.670 m 0.17 m Cnsider r is the distance frm fint O and x, then At pint x: r (0.5 r) (0.5 r) r v 344 First minima will be at: r 0.67 m f 56 19 0.67 r 0.335 m.
(c)@ 0.335 m (d) 1.00 m (e) 0.195 m Tw transmitters, S1 and S shwn in the figure, emit identical sund waves f wavelength. The transmitters are separated by a distance /. Cnsider a big circle f radius R with its center halfway between these transmitters. Hw many interference maxima are there n this big circle? / S 1 R (a)@. (b) 5. (c) 1. (d) 6. (e) 8. S 0
A listener hears tw sund waves frm tw lud-speakers that are in phase. At the listeners lcatin a phase difference f 450 is detected. What is the path difference if the wavelength f the waves is 4 m. (a) 10 m. (b)@ 5 m. (c) 99 m. (d) 1 m. (e) zer. Tw ludspeakers, S1 and S, emit sund waves f identical wavelength and amplitude. They are situated as shwn in figure 4. The tw speakers are in phase. A listener starts t walk frm pint D tward S alng a line perpendicular t the line jining S1 and S. Hw many times will he hear a minimum in sund intensity as he mves frm D t S? (a) 5 (b) (c) 1 (d)@ 4 (e) 3 1
In figure 4, tw small identical speakers are cnnected (in phase) t the same surce. The speakers are 4.10 m apart and at ear level. An bserver stands at X, 8.00 m in frnt f ne speaker. In the frequency range 00 Hz-500 Hz, the sund he hears will be mst intense if the frequency is: [speed f sund in air is 343 m/s] (a) 600 Hz. (b)@ 346 Hz. (c) 500 Hz. (d) 10 Hz. (e) 4 Hz. In figure 1, tw speakers, A and B, are driven by the same scillatr at a frequency f 170 Hz and face each ther at a distance f.0 m. What is the number f minima alng the line jining the tw surces? [Cnsider nly the ndes between the tw surces.] [Take the speed f sund in air = 340 m/s] (a)@ (b) 4 (c) 1 (d) 5 (e) zer Tw equal waves, f wavelength 4 m and amplitude A, are prduced by tw surces S1 and S as shwn in figure 1. S1 is at a distance f 3 m frm pint P and S is at a distance f 5 m frm P. When the surces are perated in phase, what is the amplitude f scillatin at P? (a) 3A/. (b)@ zer. (c) A/. (d) A. (e) A. Using: r S P S P m, (1) 1 Als: r n n(4) () frm (1) and (), ne finds n 1 fully destructive Amplitude = 0
A tne has a frequency f 1800 Hz and intensity level f 110 db in air. What is the amplitude f scillatin f air mlecules. [ f air = 1.1 kg/m 3, speed f sund in air = 343 m/s]. (a) 3.54 10-8 m. (b) 1.81 10-10 m. (c).03 10-1 m. (d).57 10-16 m. (e)@ 1.94 10-6 m. The intensity f sund waves at 5 m frm a speaker vibrating at 1000 Hz is 0.5 W/ m. Determine the displacement amplitude f the particles in the wave at that lcatin (5 m away frm the speaker). ( f air = 1.3 kg/m 3 and the speed f sund in air = 340 m/s). (a).3 10-7 m (b) 1. 10-5 m (c) 6.5 10-6 m (d)@ 7.6 10-6 m (e) 9.5 10-7 m A surce f sund (1000 Hz) emits unifrmly in all directins. An bserver 3.0 m frm the surce measures a sund level f 40 db. Calculate the average pwer utput f the surce. (a).87 10-6 W (b) 0.34 10-6 W (c) 10.5 10-6 W (d) 5.3 10-6 W (e)@ 1.13 10-6 W Cnsider tw sund waves A and B prpagating in the same medium. Find the rati f the intensity f the sund wave A t the intensity f the sund wave B if the sund level f wave A is 0 db greater than the sund level f wave B. (a) 0 (b) 15 (c) 5 (d) 10 (e)@ 100 A certain sund level is increased by 30 db. By what factr is the intensity increased? (a) 900 (b) 700 (c) 300 (d)@ 1000 (e) 30 3
Determine the intensity f a harmnic lngitudinal wave with pressure amplitude f 8.0 10-3 N/ m prpagating inside a tube filled with helium. (Fr helium: = 0.179 kg/ m 3 and speed f sund waves = 97 m/s.). (a)@ 1.8 10-7 W/ m. (b) 9. 10-8 W/ m. (c) 1.5 10-6 W/ m. (d) 3.7 10-7 W/ m. (e) 4.6 10-8 W/ m. A grup f students, in a class rm, prduce a sund level f 53 db. A single students speaking nrmally prduces a sund level f 40 db. Hw many students are in the rm? (Assume each student in the grup speaks at the same level as did the single persn.) (a) 13. (b)@ 0. (c) 30. (d) 10. (e) 5. If the distance frm a surce f sund increases by 1 meter, the sund level is decreased by db. Assume the ludspeaker that is emitting this sund emits sund in all directins. The riginal distance frm the sund surce is: (a) 1.0 m. (b)@ 3.86 m. (c) 7.7 m. (d) 1.93 m. (e) 9.93 m. 4
A 1.5 10-6 W pint surce emits sund waves istrpically. What is the sund level.5 m frm the surce? (a) 30 db. (b) 55 db. (c) 39 db. (d)@ 43 db. (e) 16 db. Find the rati f the intensities f tw sund waves if the difference in their intensity levels is 7 db. (a) 3. (b) 7. (c)@ 5. (d) 1. (e) 9. A sund surce lcated at the rigin emits sund with an average pwer f 0.04 W. Tw detectrs are lcated n the psitive x-axis. Detectr A is at x = 3.0 m and detectr B is at 5.0 m. What is the difference in sund level between A and B? (a). db (b) 3.3 db (c)@ 4.4 db (d) 5.5 db (e) 1.1 db Yu are standing at a distance D frm a pint surce f sund wave. Yu walk 30.0 m tward the surce and bserve that the intensity f these waves has dubled. Calculate the distance D. (a) 15 m. (b)@ 10 m. (c) 493 m. (d) 3 m. (e) 300 m. Which f the fllwing statements is CORRECT? (a) (b) (c) (d) The pwer transmitted by a sinusidal wave n a string decreases with increasing frequency f the wave. The speed f sund is the same in all media. Sund waves can travel in vacuum. The pwer intercepted by a sund detectr des nt depend n the area f the detectr. 5
(e)@ Electrmagnetic waves can travel in vacuum. A pint surce f a sund wave has a pwer f 0.50 W. At what distance frm the surce will the sund level be 90 db? (a) 34 m (b) 8.9 m (c) 80 m (d)@ 6.3 m (e) 40 m The intensity f sund wave A is 100 times that f sund wave B. What is the difference between their sund levels? (a)@ 0 db (b) 10 db (c) db (d) 100 db (e) 3 db If an bservers distance frm a pint surce is dubled, the sund intensity level will be: (a) increased by 6 db. (b) decreased by 4 db. (c)@ decreased by 6 db. (d) decreased by 36 db. (e) increased by 36 db. Tw waves are given by the equatins: y1(x,t) = 5.0 sin( 0.5 x + 75 t) y(x,t) = 10.0 sin( 0.50 x + 150 t) in SI units. The intensity rati f I1/I f the tw waves is: (a)@ 1/16. (b) 1/. (c) 1/3. (d) 4. (e) 1/4. The rati f the intensities f tw sund waves is 5. Find the difference in their intensity levels. (a) 1 db. (b) 4 db. (c)@ 7 db. (d) 6 db. 6
(e) db. A persn clses his windws t reduce the street nise frm 10-4 W/ m t 10-8 W/ m. What is the change in the intensity level in db? (a) - 60. (b) - 0. (c)@ - 40. (d) 40. (e) 0. I 10 Ans : 10 ln( ) 10 ln( ) 8 1 4 I 1 10 40 A pint surce emits 30 W f sund. A small micrphne has an area f 0.75 cm is placed 10 m frm the pint surce. What pwer des the micrphne receive? (a) 30 10-6 W. (b) 0.1 10-6 W. (c) 9.3 10-6 W. (d)@ 1.8 10-6 W. (e) 3.6 10-6 W. At a distance f 5.0 m frm a pint surce, the sund level is 110 db. At what distance is the sund level 95 db? (a) 7.1 m (b) 5.0 m (c) 14 m (d)@ 8 m (e) 4 m 1 Ans : 1 10 ln( ) 0 ln( ) I1 r 1 I r r 1 /0 95 110 /0 10 5.0 10 8 m r A pint surce emits sund istrpically. At a distance f 3.00 m frm the surce, the sund level is 90.0 db. What is the average pwer f the surce? (a) 1.6 mw (b) 56.5 mw (c) 8.3 mw (d)@ 113 mw (e) 315 mw The intensity f sund wave A is 800 times that f sund wave B at a fixed pint frm bth surces. If the sund level f sund A is 110 db, what is the sund level f wave B? (a) 690 db. (b) 555 db. (c) 7.3 db. (d) 50 db. (e)@ 81 db. 7
The intensity level f sund frm 10 persns each f intensity level 60 db is: (a) 1 db. (b) 10 db. (c) 600 db. (d)@ 70 db. (e) 300 db. A persn is hearing a sund level f 70 db at a distance f 3.0 m frm a pint surce. Assuming that the sund is emitted istrpically, find the pwer f the surce. (a) 8.6 10-3 W. (b).3 10-7 W. (c).9 10-4 W. (d)@ 1.1 10-3 W. (e) 7.7 10-3 W. I I /10 1 7 5 Hint: 10 10 10 10 m P 5 3 4 (3) 10 1.1 10 W W An air clumn m in length is pen at bth ends. The frequency f a certain harmnic is 410 Hz, and the frequency f the next higher harmnic is 49 Hz. Determine the speed f sund in the air clumn. (a) 317 m/s. (b) 30 m/s. (c)@ 38 m/s. (d) 34 m/s. (e) 305 m/s. An air clumn m in length is pen at ne end and clsed at the ther end. The frequency f a certain harmnic is 369 Hz, and the frequency f the next higher harmnic is 451 Hz. Determine the speed f sund in the air clumn. (a)@ 38 m/s. (b) 34 m/s. (c) 35 m/s. (d) 33 m/s. (e) 30 m/s. The secnd harmnic f a string, fixed at bth ends, f length 0.6 m and linear density 1.1 10-3 kg/m, has the same frequency as the fifth harmnic (n=5) f a pipe clsed at ne end f length 1.0 m. Find the tensin in the string. (Speed f sund = 343 m/s). (a) 90 N (b) 88 N (c) 60 N (d)@ 73 N (e) 18 N 8
During a time equal t the perid f a certain vibrating frk, the emitted sund wave travels a distance: (a) prprtinal t the frequency f the wave. (b)@ f ne wavelength. (c) f abut 331 meters. (d) directly prprtinal t the frequency f the frk. (e) equal t the length f the frk. If tw successive frequencies f a pipe, clsed at ne end and filled by air, are 500 Hz and 700 Hz, the length f the pipe is: [speed f sund in air = 340 m/s]. (a)@ 0.85 m. (b) 3.40 m. (c) 1.70 m. (d) 0.43 m. (e) 0.18 m. Which f the fllwing statements are CORRECT: 1. Waves carry energy and mmentum.. Mechanical waves need a medium t prpagate. 3. Sund waves are transverse waves. 4. A Wave n a stretched string is a lngitudinal wave. 5. Fr a tube clsed at ne end, nly dd harmnics are present. (a) 3 and 5. (b) and 4. (c) 1, and 3. (d)@ 1,, and 5. (e) 1 and 4. A 104 Hz tuning frk is used t btain a series f resnance levels in a gas clumn f variable length, with ne end clsed and the ther pen. The length f the clumn changes by 0 cm frm ne resnance t the next resnance. Frm this data, the speed f sund in this gas is: (a) 0 m/s. (b) 10 m/s. (c) 51 m/s. (d)@ 410 m/s. (e) 05 m/s. 9
A tube 1.5 m lng is clsed at ne end. A stretched wire i 30