Standing Waves Worksheet

Transcription

1 Name Date Period Stadig Waes Worksheet Show your work clearly o a separate page i ecessary. Make a sketch o the problem. Start each solutio with a udametal cocept equatio writte i symbolic ariables. Sole or the ukow ariable i a step-by step sequece.. Two childre use a homemade telephoe cosistig o two paper cups attached by a alumium wire which is 8.4 m log. Determie the time or the soud to trael rom oe cup to the other. How does this compare with the time or soud to trael the same distace through air? (speed o soud i alumium is 500 m/s, i air is 343 m/s) 8.4 m Alumium wire x t x t t t s.65ms t t 0.045s 4.5ms. A uigered guitar strig is 0.70 m log ad is tued to play E aboe middle C (330 Hz) (that is the irst harmoic). a) What is the speed o the wae o the strig? b) How ar rom the ed o this strig must the iger be placed to play A aboe middle C (440 Hz)? L = 0.7 m Air m OR L /.4m (.4)(330) 46m L 0. 55m L =? Shorter legth is as expected. Higher pitch is shorter waelegth To get a 0.55m strig, iger has to be placed = 0.75m rom ed.

2 3. A uiorm arrow tube.8 m log is ope at both eds. It resoates at two successie harmoics o requecy 75 Hz ad 330 Hz. What is the speed o soud i the gas i the tube? We oly kow that 75Hz ad 330Hz are successie harmoics; they could be the d ad the 3 rd, the 0 th ad the st,.. For a ope-ope tube, the harmoic requecies ollow the ollowig rule: 75 (.8) ( ) ( ) 330 (.8) ( ) m OR ( ) (.8) 98m 4. Someoe is sigig i a shower that measures.40 meters rom loor to ceilig, ad otices their oice causes the shower to resoate with a udametal requecy o 73 Hz. a. Sketch the stadig wae ad calculate the speed o soud i the shower? (Hit: the shower stall acts like a pipe closed at both eds).4m L / / / 73 (.4) 350.4m b. Sketch the stadig wae or the d harmoic (irst oertoe) ad calculate the requecy. L / / L 350.4/.4 46Hz.4m

3 5. A pipe orga has pipes o may dieret legths. Which pipes (log or short) do you thik would produce low requecy otes? Which would produce high requecy otes? low-log pipe, high short pipe 6. A pipe ope o both eds is resoatig to produce a ote. What could you do that would cause the same pipe to produce a ote o a dieret requecy? Describe the chage that each oe would produce i the pitch o the soud. (Hit: you should be able to idetiy at least our chages that aect the pitch.) a-temperature: Decrease i temperature iside tube would lower pitch; Icrease i temp would raise the pitch. Temperature chages the speed o soud ad thereore chages the harmoic requecies. b) Medium: chagig gas iside the tube would chage the pitch because chages the speed o soud. Put heaier gas, speed lower, pitch lower/lighter gas, speed greater, higher pitch. I illed pipe with liquid istead o gas, speed o soud would go up ery high ad harmoic requecies ad thereore pitch would icrease. c) Tube legth. Icreasig tube legth lowers the harmoic requecies ad thereore lowers the pitch. Decrease i legth raises pitch. 5. A hammer hits the ed o a bar. m log. Sketch the stadig wae o the bar or the ollowig harmoics. The speed o waes i the bar is 6,500. m/s. (Hit: The harmoic series o ibratios o a metal bar would cotai atiodes at each ed like the soud displacemet patters i a ope pipe.) MODE DIAGRAM WAVELENGTH FREQUENCY Fudametal requecy ( st harmoic) L= / =.4 m =/ =/ =6500/.4=708Hz d oertoe (3 rd harmoic) L=3 / 3 =0.8 m 3 =3/ =/ 3 =3 =6500/0.8=85Hz Resoatig with 4 odes L= 4 =0.6 m F 4 =/L =/ 4 =4 =6500/0.6=0833Hz Resoatig with 4 atiodes L=3 / 3 =0.8 m 3 =3/ =/ 3 =3 =6500/0.8=85Hz

4 6. Sketch the stadig wae patter o a resoatig object that has a ixed boudary o oe ed ad a ree boudary o the other. The legth o the resoatig object is 90.0 cm. (Note: this could be resoatig soud waes i a colum with oe closed ed ad oe ope ed) MODE DIAGRAM Number o Waes WAVELENGTH Fudametal requecy ( st harmoic) ¼ L = /4 = 3.6 m Resoatig with odes 3/4 L = 3 3 /4 3 =. m Resoatig with 3 atiodes 5/4 L = 5 5 /4 5 = 0.7 m Resoatig i 7 th harmoic 7/4 L = 7 7 /4 7 = 0.54 m 7. Describe the type o pipe that would hae the stadig waes described i each situatio below. a) The wae has displacemet atiodes at both eds o the tube. ope-ope tube (both eds ope) b) The wae has a displacemet atiode at oe ed o the tube ad a ode at the other ed o the tube. Oe ope ed, oe closed ed c) The wae has displacemet odes at both eds o the tube. Closed-closed (both eds closed) 8. While driig to work, Jill otices that workers hae strug plastic ribbo aroud their worksite to preet people rom walkig ito the hole. Jill otes that betwee two support poles the ribbo is.5 m log ad is ibratig i a stadig wae patter with 5 loops ad that the ibratig ribbo is creatig a soud that correspods to the ote A ( = 40 Hz). a. What is the waelegth o the stadig wae?.5m 5 L m

5 b. What is the speed o ibratios i the ribbo? 5 5 L ( 0.6)(40) 5m/ s 5.5 (40) 5m/ s 9. A spaceship lads o a ew plaet. The crew decides to measure the speed o soud i the plaets atmosphere. Takig a tube with a legth o 50 cm, they id that oe resoat requecy occurs at,50 Hz, ad the ext resoat requecy at,940 Hz. What is the speed o the soud? What is the umber o each harmoic? What type o pipe is the crew usig (ope-ope, ope-closed, closedclosed)? 50 Hz ad 940Hz are successie harmoics. We do t kow which harmoics they are. Could be the st ad d, the 5 th ad 6 th, the 99 th ad 00 th. There is a patter or the harmoic requecies o soud i pipes: th harmoic For ope-ope pipes AND closed-closed pipes For closed-ope pipes: (or all ) (oly or ODD ) Ope-ope or Closed-closed 50 (0.5) ( ) 940 (0.5) ( ) m Kowig the elocity, we must id which harmoics these are. To do so plug the elocity ito the harmoic equatios to id (40) 50 (0.5) Thereore 50Hz is the 6 th harmoic ad 940Hz is the 7 th harmoic i a ope-ope pipe or a closed-closed pipe. V=40 m/s

6 Closed-ope (odd harmoics) Kowig the elocity, we must id which harmoics these are. To do so plug the elocity ito the harmoic equatios to id. EVEN harmoics DO NOT resoate i a closed-ope pipe so it is NOT a closed-ope pipe 0. The predomiat requecy o a certai police car s sire is 800 Hz whe at rest. What requecy do you detect i you moe with a speed o 30 m/s (a) toward the car ad (b) away rom the car? Towards the sire: 50 4(0.5) ( ) 940 4(0.5) ( ) m 50 0 / (40) 50 4(0.5) s = 800 Hz d =30m/s D Source + Detector Expect a Doppler shit to higher requecies: D D S Hz S Away rom the sire: Expect a Doppler shit to lower requecies D D S Hz S 343 0