Standing Waves.

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Presentation transcript:

Standing Waves

Two pulses are shown traveling in opposite directions along a string. Each is moving with a velocity of 1.0 cm/s. After 4.0 s, the string will look like which diagram? Ans: #2

f1 = v/2L for a fixed string so f1 = 692.8 m/s / (2*0.80m) = 433 Hz A guitar string 80.0 cm long has a mass of 25.0 g. When tuned it is under a tension force of 15 kN. What will be the fundamental frequency of this string when played? What will be the next 3 harmonic frequencies for this string? Need to know the velocity. v = √ F/μ Then find the fundamental frequency. v = √15 x 103 N / (.025 kg/.80 m) = 692.8 m/s f1 = v/2L for a fixed string so f1 = 692.8 m/s / (2*0.80m) = 433 Hz A fixed string produces all harmonics so the next 3 will be: f2 = 2(433 Hz) f3 = 3(433 Hz) f4 = 4(433 Hz)

A stretched string is fixed at points 1 and 5 A stretched string is fixed at points 1 and 5. When vibrating at the 2nd harmonic frequency, the nodes of the standing wave are at points: 1,3 and 5 If the string is 1.5 m long and a wave will travel at 300 m/s, what is the frequency of the 2nd harmonic? The fundamental, f1 = v/2L so f1 = 100 Hz. A fixed string produces all harmonics so the 2nd, f2 = 2(f1) or 200 Hz.

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 4th harmonic is shown in: ___ This represents the ? overtone. The 5th harmonic is: #4 3rd #5

closed #4 #2 Not here #3 The figure represents a column of length L, Vibrating in several harmonics. Is this a closed or open end instrument? The 7th harmonic is: The first overtone is: The 4th harmonic is: The second overtone is: closed #4 #2 Not here #3

Identify the harmonic and overtone in each diagram. none Of the sound sources shown, which is vibrating with its first harmonic: Its third harmonic: The 2nd harmonic: Identify the harmonic and overtone in each diagram. none The rod and whistle Not here Whistle: 3rd H, 1st O pipe: 2nd H, 1st O string: 2nd H, 1st O rod: 3rd H, 1st O

Standing waves exist in a closed-end pipe of length L Standing waves exist in a closed-end pipe of length L. The speed of the waves on the string is v. The three lowest frequencies of vibration are: a. v/4L v/2L 3v/4L b. v/4L 3v/4L 5v/4L c. v/2L 2v/2L 3v/2L d. v/L 2v/2L 2v/3L

Which pipe shown will produce the lowest pitch? closed open closed open L = 1.0 m L = 1.0 m L = 0.5 m L = 0.5 m Ans: must produce the longest λ so the 1.0 m closed pipe Remember: closed starts with ¼ λ