Physics 1C. Lecture 14B

Transcription

1 Physics 1C Lecture 14B "I did never know so full a voice issue from so empty a heart: but the saying is true 'The empty vessel makes the greatest sound'." --William Shakespeare

2 Doppler Effect Why does an ambulance siren moving towards you sound different than when it is moving away from you? It is wave property of sound. Let s say there is a stationary source that is emitting sound at a certain frequency. Observers on either side of the source observe the same frequency (λ is the same for both). O1 s O2 f = v sound λ

3 Doppler Effect But what if the source is moving to the left, then: O1 v s s O2 Observer 1 believes that the wavelength has decreased (compared to before): f 1 = v sound increased λ 1 decreased Observer 2 believes that the wavelength has increased (compared to before): decreased f 2 = v sound λ 2 increased

4 Doppler Effect We find that for a source moving: v f o = f sound s v sound m v s where f o is the frequency the observer detects, f s is the frequency the source emits, v s is the velocity of the source, v sound is the velocity of the sound wave. Use if the source is moving toward the observer and use + if the source is moving away from the observer. We can also have the observer moving toward or away from the source.

5 Doppler Effect We find that for an observer moving: v f o = f sound ± v o s v sound where v o is the velocity of the observer. Use + if the observer is moving toward the source and use if the observer is moving away from the source. For complicated cases (both moving) use: v f o = f sound ± v o s v sound m v s Just remember: top sign (toward) bottom sign (away)

6 Doppler Effect Example Two submarines are underwater and approaching each other head-on. Sub A has a speed of 12.0m/s and sub B has a speed of 8.00m/s. Sub A sends out a 1550Hz sonar wave that travels at a speed of 1520m/s. What is the frequency detected by sub B? Answer Define a coordinate system (choose observer and source). Choose the sub A as source and sub B as the observer.

7 Doppler Effect Answer Since they are moving toward each other use top sign: v f o = f sound ± v o s v sound m v s f o =1550Hz 1520 m s + 8 m s 1520 m s 12 m s f o =1550Hz 1528 m s 1508 m s =1550Hz 1.01 ( ) =1570Hz The frequency has increased, according to the observer.

8 Clicker Question 14B-1 Karla and Max are both listening to the source of sound waves that is moving to the right at 10m/s. Compare the frequencies each hears. A) f Karla > f Max. B) f Karla = f Max. C) f Karla < f Max. Karla s 10m/s Max

9 Standing Waves When you have waves reflected back (such as on a rope or in air), these waves can interfere. At proper frequencies you can create standing wave (which have nodes and anti-nodes). Nodes are parts of the medium that do not move. Anti-nodes are parts of the medium that will vibrate between A and A.

10 Standing Waves on a String For a string fixed at both ends, the longest standing wave we can achieve is: The frequency for this standing wave is known as first fundamental frequency. The length, L, of the string is equal to one-half the wavelength. We label standing waves by the number of antinodes, so this wave is n=1.

11 Standing Waves on a String The next longest wavelength that we can achieve on this string is n=2. Here, L= λ The next longest wavelength that we can achieve on this string is n=3. Here, L= (3/2)λ

12 Standing Waves on a String For the nth frequency: L = n 2 λ n =1, 2, 3, 4... λ = 2 n L Recall that: v = λf So in general the frequency will be: f n = v λ = nv 2L f n = n v 2L The different frequencies are known as harmonics for standing waves. Just choose n=5 if you want a standing wave with 5 anti-nodes.

13 Interference Sound waves from different sources can interfere with one another. We can assume that the sources of the sound waves start the same (i.e. are in phase). The cause of this interference is path length difference (Δr = r 2 - r 1 ). Your location determines what sound you hear.

14 Interference If the path length difference between the two waves is zero or some integer multiple of wavelengths then you will get constructive interference (loud sound). Δr = nλ If the path length difference between the two waves is an odd half number of wavelengths then you will get destructive interference (little or no sound). Δr = ( n + 1 2)λ

15 Sound Interference Example Two loudspeakers are 2.0m apart and are driven by the same oscillator. Both speakers emit 700Hz sound waves into a room where the speed of sound is 341m/s. A listener stands 5.0m in front of the speakers and 2.0m to one side of the center. Does the listener experience constructive interference, destructive interference, or neither at this location?

16 Sound Interference Answer We are looking to calculate the path length difference, Δr. So we should calculate the difference between r 2 and r 1. Speaker 1 r 1 5m 1m Speaker 2 r 2 5m 3m

17 Sound Interference Answer Next, we should see how many multiples of the wavelength this path length difference is (integer, half-integer, or neither). So we should calculate the wavelength of this sound wave. Comparing this to the path length difference gives: <- Rounding to three places The path length difference at this location is a halfinteger wavelength, so we should have destructive interference.

18 For Next Time (FNT) Start reading Chapter 21 Keep working on the homework for Chapter 14