Tuesday 1 Dec:

 Journal:

 

 

 

You have a standing wave in a tube (movable: one end closed). Speed of sound = 340m/s

 

a) Draw first 2 harmonics.

b) If the shortest length of air column that produces a resonance is 1.8m and the next shortest length is 3.8m, what is the l of the standing wave?

c) What is the frequency of the standing wave?

 

 

 

 

 

 

 

 

 

 

 

 

 

B) L2 - L1 = 1/2l

 

(3.8m - 1.8m) (2) = l

 

l = 4.0m

 

 

C) V = (F)(l)

     340 m/s = F (4m)

 

       F = 85.0 Hz

 

Notes:

1. A person stands between two speakers driven by the same source.  Each speaker produces a tone with a frequency of 200 Hz on a day when the speed of sound is 330 m/s.  If a person is 1.61 m from one speaker, how far (the two closest locations) from the other speaker does the person sense:

a) Constructive

b) Destructive interference

 

 

 

 

 

 

 

 

First find l:

     v = lf

      l = v/f  --> 330/200

      l =  1.65m

     

Constructive interference: (Where two waves crests or troughs meet). Location must be an even l apart (i.e., 1.65m, 3.3m, 4.95m, etc). The difference in distance between the two speakers from the observer must be l apart.

So closest two points are: 1.61 m +- 1.65m = 3.26 m & 4.91m

 

Destructive interference: (Where a waves crest and trough meet). Location must be an ½l apart (i.e., .31m, 0.92m, 1.5m, etc). The difference in distance between the two speakers from the observer must be ½l apart.

So closest two points are: 1.61 m +- 0.8m = 0.81 m & 2.41 m

 

 

 

2. A standing wave of 5 segments, as is set on a string 10 meters long.

a. What is the wavelength (l)?

 

 

b. What is the wave’s velocity, if the fundamental frequency is 15Hz?  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a.       Two Segments = one l. Therefore, 2/5 of 10m   is 4.0m

b.     Fundamental l:   

     One segment = 10m = 1/2 l,

     therefore one Fundamental l is 20.0m

     V = f l à  V = (15)(20) = 300m/s

 

 

3. An instrument plays a note and has the following Frequency Spectrum for that note: 200, 400, 600, 800… The instrument most likely would be:

               

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

        

 These are direct multiples of the Fundamental  Frequency. Only possible with a string and/or a wind, open ended tube.

1st, 2nd, 3rd, (etc.) harmonics.

 

Tube with one closed end is 1st, 3rd, 5th harmonics

           

 

4. What characteristic of the sound (Frequency, Amplitude, Wavelength, Period) as you move toward a speaker emitting a pure tone?

a. If you move slowly

b. If you move quickly

 

 

 

 

 

 

 

 

 

 

 

a.  Freq: (same), Amplitude: (up),  l: (same), T: (same)

b. Freq: (up), Amplitude: (up),  l: (shorter), T: (shorter)

 

 

 

 

5. What happens to the of a wave's velocity on a stretched string when the tension in a string is increased by 9 times?

 

 

 

 

 

 

 

 

 

 

 

V = √ T/ML   (velocity of waves on a string)

 

 

 

 

Increase by √9 = 3 times the velocity

 

 

 

 

 

 

 

 

6. What happens if the string’s mass is doubled?

 

 

 

 

 

 

 

 

 

 

 

V = √ T/ML

    V goes down by √1/2

                                       

 

 

 7. In the Doppler affect for sound waves, factors that affect the frequency that the observer hears include?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I. The speed of the source

II. The speed of the observer

 

 

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