Presentation on theme: "Long spring A wave travels down a long spring at a speed of 20 m/s. It is generated by a hand moving up and down 10 times per second, with a total displacement."— Presentation transcript:
Long spring A wave travels down a long spring at a speed of 20 m/s. It is generated by a hand moving up and down 10 times per second, with a total displacement of 6 cm. At time zero, the hand is at the lowest point. Find an equation describing the vertical displacement of the spring as a function of position and time.
Speed of wave on a string Elastic forces Mass per length of string A piano string is under a tension of about 2000 N, with a mass of 2.5 g per meter of length. Determine the speed of the transverse wave on this string.
Speed of wave on a string Consider a long string consisting of a thin and a thick segment. Which of the three quantities will change, if …the wave passes from the thin to the thick segment? …the frequency of the source changes?
Reflection at a fixed end Reflected pulse is inverted
Reflection at a loose end Reflected pulse is not inverted
Superposition of waves
Constructive and destructive superposition
Standing waves on strings A string of length L, fixed at both ends, has resonance frequencies: Fundamental 1 st Harmonic 1 st overtone 2 nd Harmonic 2 nd overtone 3 rd Harmonic Eigen frequencies of the string:
Length of the piano string The speed of transverse waves on a piano string is 942 m/s. How long does this string have to be in order to generate a sound Hz (middle C)?
Resonances of tubes Fundamental 1 st overtone Closed tubes open tubes
Sound and hollow tubes Sound: transverse wave, compression wave node Loop at open end node Loop at open end Both ends open: One end closed: