Introduction to Waves

How do you describe the motion of a pulse traveling through the slinky? Watch the video clip: Making_PulsesMaking_Pulses Sketch what you observe. Draw a picture of a pulse and label the parts including: amplitude and equilibrium (rest position).

How do you describe the motion of a pulse traveling through the slinky? Watch the video clip: Making_PulsesMaking_Pulses Sketch what you observe. Draw a picture of a pulse and label the parts including: amplitude and equilibrium (rest position). Equilibrium position Amplitude Pulse Length

Is the speed of a pulse constant? Propagating_Pulses.mov Create a position vs. time graph. Use the meterstick in the background for a distance scale. The video frame rate is 30 frames per second, so the time elapsed between frames is 1/30 s.

Pulse Speed The graph should be linear… so the speed is constant!

How do you describe the motion of a particle in the spring as a pulse passes through? Tie a string to the midpoint of a slinky. Send a pulse through the slinky and describe the movement of the string.

How do you describe the motion of a particle in the spring as a pulse passes through? Motion of particle in spring/slinky is perpendicular to the motion of the pulse! We call this a TRANSVERSE pulse.

What is the difference between a pulse and a wave? Pulse = Single event Wave = Multiple pulses sent continuously Pulse Wave Wave length = Amplitude Pulse length

How do you calculate the speed of a pulse/wave? 1. Speed = distance / time 2. Speed = wavelength * frequency = f 3. Speed = T= tension of string/slinky  = linear mass density or mass/length

Fixed and Free End (Assuming no Friction) What happens to the amplitude of a pulse as it travels down the slinky and back? What happens to the speed of a pulse as it travels down the slinky and back?

Fixed and Free End (Assuming no Friction) What happens to the amplitude of a pulse as it travels down the slinky and back? Stays the same What happens to the speed of a pulse as it travels down the slinky and back?

Fixed and Free End (Assuming no Friction) What happens to the amplitude of a pulse as it travels down the slinky and back? Stays the same What happens to the speed of a pulse as it travels down the slinky and back? Stays the same

Fixed vs. Free End What is the shape of the pulse after it comes back down the slinky after hitting the fixed end? Fixed End What is the shape of the pulse after it comes back down the slinky after hitting the free end? Free End Free End

Fixed vs. Free End What is the shape of the pulse after it comes back down the slinky after hitting the fixed end? Inverted What is the shape of the pulse after it comes back down the slinky after hitting the free end? Upright

Interacting at a Boundary–Reflection and Transmission Involving Two Media Condition Reflection (I or U) Transmission (I, U or N) Slinky  Fixed End Slinky  Snaky Snakey  Slinky Snakey  Free End

Interacting at a Boundary–Reflection and Transmission Involving Two Media ConditionReflectionTransmission Slinky  Fixed EndInvertedNone Slinky  Snaky Snakey  Slinky Snakey  Free End

Interacting at a Boundary–Reflection and Transmission Involving Two Media ConditionReflectionTransmission Slinky  Fixed EndInvertedNone Slinky  SnakyInvertedUpright Snakey  Slinky Snakey  Free End

Interacting at a Boundary–Reflection and Transmission Involving Two Media ConditionReflectionTransmission Slinky  Fixed EndInvertedNone Slinky  SnakyInvertedUpright Snakey  SlinkyUprightUpright Snakey  Free End

Interacting at a Boundary–Reflection and Transmission Involving Two Media ConditionReflectionTransmission Slinky  Fixed EndInvertedNone Slinky  SnakyInvertedUpright Snakey  SlinkyUprightUpright Snakey  Free EndUprightNone

Superposition- What happens when waves or pulses interact? 1. Two pulses from opposite sides: opposite superpositionopposite superposition 2. Two pulses from same side: same superpositionsame superposition

Superposition- What happens when waves or pulses interact? 1.Two pulses from opposite sides: 2. Two pulses from same side: same superposition same superposition

Superposition- What happens when waves or pulses interact? 1.Two pulses from opposite sides: 2. Two pulses from same side:

Standing Waves When we send pulses down string or slinky at certain frequencies we produce standing waves… let’s see an example. Standing Wave MovieStanding Wave Movie

Do you see a pattern for calculating frequency for each standing wave? Length of String (m) Speed (m/s)Sketches (m) Frequency =? f = v/ 56.02* L or 10 m f = v/2L 0.6 Hz 56.01L or 5m f = v/L 1.2 Hz /3 L or 3.33m f = 3v/2L 1.8 Hz 56.0½ L or 2.5 m f = 2 v/L 2.4 Hz 56.02/5 L or 2 m f = 5v/2L 3 Hz

Two Fixed End Standing Waves Frequency for a standing wave produced with two fixed ends with n antinodes. n = 1, 2, 3… Node Antinode

What if only one end was fixed…

Do you see a pattern for calculating frequency for each standing wave? Length of String (m) Sketches (m) Frequency =? f = v/ L4L f = v/4L L4/3 L f = 3v/4L L4/5 L f = 5v/4L L4/7 f = 7 v/4L L4/9 f = 9v/4L

One Fixed End Standing Waves Frequency for a standing wave produced with one fixed end n = 1, 3, 5…

Sound! Two major differences Longitudinal Wave Speed

Speed of Sound Speed = B = bulk modulus is the mathematical description of an object or substance's tendency to be deformed elastically  = density Sound is faster in a more elastic and less dense medium.

Sound is a Longitudinal Wave Particle motion is parallel to motion of wave or pulse.

Superposition Amplitude = Loudness… Constructive Interference = LOUD Destructive Interference= no sound

Interference of Sound Waves Constructive Interference: Path Difference is zero or some integer multiple of wavelengths  d = 0, 1, 2, 3,…. Destructive Interference: Path Difference is ½, 1 ½, 2 ½, etc wavelengths  d = ½, 3/2, 5/2,….

Path length difference is 0. Two wave crests will meet creating constructive. LOUD Path length difference is 1/2. Wave crest and trough will meet creating destructive interference…. No sound /2

Interference Example Two speakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, which is located 8.00 m from the center of the line connecting the two speaker. The listener then walks to point P, which is perpendicular to the distance m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take the speed of sound in air to be 343 m/s. (Minimum = no sound) 3.0 m O 8.0 m P m

Interference Example Two speakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, which is located 8.00 m from the center of the line connecting the two speaker. The listener then walks to point P, which is perpendicular to the distance m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take the speed of sound in air to be 343 m/s. (Minimum = no sound) 3.0 m O 8.0 m P m Path length for speaker 2 = 8.08 m Path length for speaker 1 =8.211

Interference Example Two speakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, which is located 8.00 m from the center of the line connecting the two speaker. The listener then walks to point P, which is perpendicular to the distance m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take the speed of sound in air to be 343 m/s. (Minimum = no sound) 3.0 m O 8.0 m P m Path length for speaker 2 = 8.08 m Path length for speaker 1 =8.21Path length difference = 0.13 m

Interference Example Two speakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, which is located 8.00 m from the center of the line connecting the two speaker. The listener then walks to point P, which is perpendicular to the distance m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take the speed of sound in air to be 343 m/s. (Minimum = no sound) Path length difference = 0.13 m First minimum occurs when the difference is /2 so… m = /2  = 0.26 m = 0.26 m V = 343 m/s So f = 1.3 kHz

Two identical loudspeakers face each other at a distance of 180 cm and are driven by a common audio oscillator at 680 Hz. Locate the points between the speakers along a line joining them for which the sound intensity is (a) maximum (b) minimum. Assume the speed of sound is 340 m/s.

Beats

Doppler Effect

Shock Waves

Standing Waves for Sound Can you find the pattern for the harmonic frequencies? Sometimes called fundamental frequency. Sometimes called first overtone. Sometimes called second overtone.

Standing Waves for Sound Can you find the pattern for the harmonic frequencies? n= 1, 2, 3… Sometimes called fundamental frequency. Sometimes called first overtone. Sometimes called second overtone.

Standing Waves for Sound (Closed End) Can you find the pattern for the harmonic frequencies? N = 1, 3, 5, etc Sometimes called fundamental frequency. Sometimes called 1st overtone. Sometimes called 2 nd overtone.

Intensity Intensity is average power/ area = P/4  r^2