Physics B Waves and Sound Name: AP Review. Show your work:

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1 Physics B Waves and Sound Name: AP Review Mechanical Wave A disturbance that propagates through a medium with little or no net displacement of the particles of the medium. Parts of a Wave Crest: high point Trough: low point Equilibrium: mid point Amplitude: distance from equilibrium to crest or trough Wavelength: distance between adjacent crests Speed of a wave The speed of a wave is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. v = d/t d: distance t: time v = λƒ v : speed (m/s) λ : wavelength (m) ƒ : frequency (s 1, Hz) Period of a wave T = 1/ƒ T : period (s) ƒ : frequency (s-1, Hz) Wave types A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction the wave moves. Example: waves on a string A longitudinal wave (also called a compression wave) is a wave in which particles of the medium move in a direction parallel to the direction the wave moves. Example: sound Problem: Wavelength and frequency (1993) 52. A radar operates at a wavelength of 3 centimeters. The frequency of these waves is (A) Hz (B) 10 6 Hz (C) 10 8 Hz (D) 3 x 10 8 Hz (E) Hz Reflection of waves Occurs when a wave strikes a medium boundary and bounces back into original medium. Completely reflected waves have the same energy and speed as original wave. Fixed-end reflection: wave reflects with inverted phase. This occurs when reflecting medium has greater density. Open-end reflection: wave reflects with same phase. This occurs when reflecting medium has lesser density. Light Light is also a wave, but it is an electromagnetic wave that requires no medium through which to travel. It is transverse in its geometry. 4/13/2011 Waves and Sound-1 Bertrand

2 Problem: Reflection of Waves (1998) 29. One end of a horizontal string is fixed to a wall. A transverse wave pulse is generated at the other end, moves toward the wall as shown above, and is reflected at the wall. Properties of the reflected pulse include which of the following? I. It has a greater speed than that of the incident pulse. II. It has a greater amplitude than that of the incident pulse. III. It is on the opposite side of the string from the incident pulse. Problem: Refraction of Waves (1998) 27. When light passes from air into water, the frequency of the light remains the same. What happens to the speed and the wavelength of light as it crosses the boundary in going from air into water? Speed (A) Increases (B) Remains the same (C) Remains the same (D) Decreases (E) Decreases Wavelength Remains the same Decreases Remains the same Increases Decreases (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III Refraction of waves Transmission of wave from one medium to another. Refracted waves may change speed and wavelength. Refracted waves do not change frequency. Principle of Superposition When two or more waves pass a particular point in a medium simultaneously, the resulting displacement at that point in the medium is the sum of the displacements due to each individual wave. The waves interfere with each other. Types of interference. If the waves are in phase, that is crests and troughs are aligned, the amplitude is increased. This is called constructive interference. If the waves are out of phase, that is crests and troughs are completely misaligned, the amplitude is decreased and can even be zero. This is called destructive interference. Sounds in the Real World Because of superposition and interference, real world waveforms may not appear to be pure sine or cosine functions. That is because most real world sounds are composed of multiple frequencies. 4/13/2011 Waves and Sound-2 Bertrand

3 Standing Wave A standing wave is a wave that is reflected back and forth between fixed ends (of a string or pipe, for example). Reflection may be fixed or open-ended. Superposition of the wave upon itself results in constructive interference and an enhanced wave. Problem: Superposition (1988) Problem: Superposition (1993) 59. The figure above shows two wave pulses that are approaching each other. Which of the following best shows the shape of the resultant pulse when the centers of the pulses, points P and Q. coincide? 28. Two wave pulses, each of wavelength λ, are traveling toward each other along a rope as shown above. When both pulses are in the region between points X and Y. which are a distance λ apart, the shape of the rope will be which of the following? 4/13/2011 Waves and Sound-3 Bertrand

4 Problem: Wave on a string (1993) 32. Two sinusoidal functions of time are combined to obtain the result shown in the figure above. Which of the following can best be explained by using this figure? A standing wave of frequency 5 hertz is set up on a string 2 meters long with nodes at both ends and in the center, as shown above. 27. The speed at which waves propagate on the string is (A) 0.4 m/s (B) 2.5 m/s (C) 5 m/s (D) 10 m/s (E) 20 m/s (A) Beats (B) Doppler effect (C) Diffraction (D) Polarization (E) Simple harmonic motion Problem: Standing wave (1993) 28. Farsighted and Nearsighted Resonance Occurs when a vibration from one oscillator occurs at a natural frequency for another oscillator. The first oscillator will cause the second to vibrate. Doppler Effect The Doppler Effect is the raising or lowering of the perceived pitch of a sound based on the relative motion of the observer and the source of the sound. When an ambulance is racing toward you, the sound of its siren appears to be higher in pitch. When the ambulance is racing away from you, the sound of its siren appears to be lower in pitch. Beats The characteristic loud-soft pattern that characterizes two nearly (but not exactly) matched frequencies. Problem: Interference (1988) 4/13/2011 Waves and Sound-4 Bertrand

5 Problem: Doppler Effect (1993) 58. In the Doppler effect for sound waves, factors that affect the frequency that the observer hears include which of the following? I. The speed of the source II. The speed of the observer III. The loudness of the sound (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III Diffraction The bending of a wave around a barrier. Diffraction of light combined with interference of diffracted waves causes diffraction patterns. Double-slit or multi-slit diffraction nλ = d sinθ n: number of bright spot (the center one is n=0) λ: wavelength (m) d: spacing between slits (m) θ: angle defined by bright spot n, the diffraction grating, and the central bright spot Note: Although it is most commonly applied to light, the diffraction equation also works for sound or other mechanical waves. Problem: Diffraction (1998) Problem: Doppler Effect (1998) 51. Plane sound waves of wavelength 0.12 m are incident on two narrow slits in a box with nonreflecting walls, as shown above. At a distance of 5.0 m from the center of the slits, a first-order maximum occurs at point P, which is 3.0 m from the central maximum. The distance between the slits is most nearly 49. A small vibrating object on the surface of a ripple tank is the source of waves of frequency 20 Hz and speed 60 cm/s. If the source S is moving to the right, as shown above, with speed 20 cm/s, at which of the labeled points will the frequency measured by a stationary observer be greatest? (A) A (B) B (C) C (D) D (E) It will be the same at all four points. (A) 0.07 m (B) 0.09 m (C) 0.16 m (D) 0.20 m (E) 0.24 m 4/13/2011 Waves and Sound-5 Bertrand

6 << ADVANCED TOPIC >> Single-slit diffraction These are much less well defined patterns Large central bright spot surrounded by dark bands nλ = s sinθ n: number of dark band (the central bright spot is n=0; all other n s are dark bands) λ: wavelength (m) s: width of slit (m) θ: angle defined by dark band n, the slit, and the central bright spot Problem: Single-slit diffraction (1988) 27. Which of the following is true of a single-slit diffraction pattern? (A) It has equally spaced fringes of equal intensity. (B) It has a relatively strong central maximum. (C) It can be produced only if the slit width is less than one wavelength. (D) It can be produced only if the slit width is exactly one wavelength. (E) It can be produced only if the slit width is an integral number of wavelengths. 4/13/2011 Waves and Sound-6 Bertrand