# Differences

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 phy131studiof15:lectures:chapter18 [2015/07/22 11:35]mdawber [Reflection and transmission] phy131studiof15:lectures:chapter18 [2015/11/09 08:51] (current)mdawber [Interference between two speakers] Both sides previous revision Previous revision 2015/11/09 08:51 mdawber [Interference between two speakers] 2015/11/09 08:51 mdawber [Interference between two speakers] 2015/11/09 08:42 mdawber [Reflection and transmission] 2015/11/09 08:41 mdawber [Reflection and transmission] 2015/11/05 16:48 mdawber [Beats] 2015/11/05 16:46 mdawber [Open and closed pipes] 2015/11/05 14:09 mdawber [Standing Waves on a String - Both ends fixed] 2015/11/05 14:07 mdawber [Interference between two speakers] 2015/07/22 11:37 mdawber [A flaming tube] 2015/07/22 11:35 mdawber [Reflection and transmission] 2015/07/22 11:34 mdawber [Principle of Superposition] 2015/07/22 11:32 mdawber created Next revision Previous revision 2015/11/09 08:51 mdawber [Interference between two speakers] 2015/11/09 08:51 mdawber [Interference between two speakers] 2015/11/09 08:42 mdawber [Reflection and transmission] 2015/11/09 08:41 mdawber [Reflection and transmission] 2015/11/05 16:48 mdawber [Beats] 2015/11/05 16:46 mdawber [Open and closed pipes] 2015/11/05 14:09 mdawber [Standing Waves on a String - Both ends fixed] 2015/11/05 14:07 mdawber [Interference between two speakers] 2015/07/22 11:37 mdawber [A flaming tube] 2015/07/22 11:35 mdawber [Reflection and transmission] 2015/07/22 11:34 mdawber [Principle of Superposition] 2015/07/22 11:32 mdawber created Line 12: Line 12: A one dimensional pulse on a string which reaches the end of string will be reflected. The direction of the pulses displacement depends on the boundary condition where the reflection takes place, ie. whether the string is fixed or free. A one dimensional pulse on a string which reaches the end of string will be reflected. The direction of the pulses displacement depends on the boundary condition where the reflection takes place, ie. whether the string is fixed or free. - This can be demonstrated on the Shive wave machine. + This can be [[http://​www.animations.physics.unsw.edu.au/​jw/​waves_superposition_reflection.htm|demonstrated on the Shive wave machine.]] When a wave encounters a change in medium there will be some partial reflection with a phase change that depends on whether it is being reflected from a more or less resistive medium ​ . When a wave encounters a change in medium there will be some partial reflection with a phase change that depends on whether it is being reflected from a more or less resistive medium ​ . - We can also look at reflection in 2 dimensions, in a [[http://​www.falstad.com/​ripple/​|virtual ripple tank]]. - Here we find that the angle of reflection is equal to the angle of incidence. =====Spatial Interference ===== =====Spatial Interference ===== Line 47: Line 45: - If the waves propagate from the source in all 3 dimensions then we need to take in to account that  as we showed in [[phy141:lectures:27&#​energy_in_a_wave|lecture 27]], $A\propto\frac{1}{r}$. To determine [[phy141:lectures:29&#​loudness_and_decibels|perceived loudness]] we need to remember that it depends logarithmically on intensity. I have factored these considerations in the following calculations I performed in Maple. The patterns are for two speakers separated by 1m. + If the waves propagate from the source in all 3 dimensions then we need to take in to account that  as we showed in [[phy131studiof15:lectures:chapter17|chapter 17]], $A\propto\frac{1}{r}$. To determine [[phy131studiof15:lectures:chapter17&#​loudness_and_decibels|perceived loudness]] we need to remember that it depends logarithmically on intensity. I have factored these considerations in the following calculations I performed in Maple. The patterns are for two speakers separated by 1m. {{speakerinteference.png}}\\ {{speakerinteference.png}}\\ Line 75: Line 73: ​**Ramp from 400 to 1200Hz**\\ ​**Ramp from 400 to 1200Hz**\\ + + + ===== 18.P.014 ===== Line 110: Line 111: Recall that for waves on a string $v=\sqrt{\frac{F_{T}}{\mu}}$ so if you take a string and stretch it further you need to take in to account both changes in $l$ and $v$. Recall that for waves on a string $v=\sqrt{\frac{F_{T}}{\mu}}$ so if you take a string and stretch it further you need to take in to account both changes in $l$ and $v$. + + ===== 18.P.016 ===== + ===== Making Sound - String Instruments ===== ===== Making Sound - String Instruments ===== Line 124: Line 128: + ===== 18.P.043 ===== + + ===== 18.P.047 ===== ===== A flaming tube ===== ===== A flaming tube ===== Line 136: Line 143: It's worth noting that as the speed of sound is $v=\sqrt{\frac{B}{\rho}}$ and the density $\rho$ can be approximated as the propane pressure the standing wave frequencies depend on the propane pressure and will not be the same as the frequencies when the tube is just full of air at external pressure. It's worth noting that as the speed of sound is $v=\sqrt{\frac{B}{\rho}}$ and the density $\rho$ can be approximated as the propane pressure the standing wave frequencies depend on the propane pressure and will not be the same as the frequencies when the tube is just full of air at external pressure. + + + ===== Beats===== + + + [[http://​www.phys.unsw.edu.au/​jw/​beats.html|Beats]] occur when two waves with frequencies close to one another interfere. + + If the two waves are described by + + $D_{1}=A\sin2\pi f_{1}t$ + + and + + $D_{2}=A\sin2\pi f_{2}t$ + + $D=D_{1}+D_{2}$ + + Using $\sin\theta_{1}+\sin\theta_{2}=2\sin\frac{1}{2}(\theta_{1}+\theta_{2})\cos\frac{1}{2}(\theta_{1}-\theta_{2})$ + + $D=2A\cos2\pi(\frac{f_{1}-f_{2}}{2})t\sin2\pi(\frac{f_{1}+f_{2}}{2})t$ + + A maximum in the amplitude is heard whenever $\cos2\pi(\frac{f_{1}-f_{2}}{2})t$ is equal to 1 or -1. Which gives a beat frequency of $|f_{1}-f_{2}|$. + + ===== 18.P.057 ===== + + + ===== Can you hear the beat? ===== + + Typically when two tones are seperated by less than about 30-40Hz we hear beating, if the separation is more than that they tend to sound like to different tones. (You can try a similar experiment at a higher frequency at [[http://​www.phys.unsw.edu.au/​jw/​beats.html|Beats from Physclips]]). + + + <​html>​ +