13.1 Classification of Waves A. Identify whether each statement is true or false. 1. Sound waves are transverse waves. FALSE 2. A wave is said to be in equilibrium when its particles compress and undergo rarefaction in a chain. 3. Mechanical waves are caused by the disturbance of transfer of energy from one point to another using a medium. 4. A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. 5. A medium is a substance or material that causes the disturbance to produce waves. 13.2. Sinusoidal Wave Function A. Identify whether each statement is true or false. 1. 2. The distance covered by a particle is a function of t and x, such that y : y (x, t). The differences between the cyclic motions of a wave at different points on a string are called path differences. The wave number is expressed in radians per second. 4. The phase of a particle's motion on different positions of awave is the same. 10. The sinusoidal wave function traveling in the direction of the horizontal axis is equal to Amman When a sinusoidal wave along a string is displaced from left to rightI each particle has a frequency inversely proportional to the amplitude. Angular frequency is expressed in units of radians per meter. The cyclical wave motions at various points on a string are synchronized and regular. For two particles on a string, the particle's motion on the right falls behind the particle's motion on the left with a value proportional to the distance between the two particles. The sinusoidal wave function is expressed in terms of the wave number through the relation Ami 4\". B. Solve the following problems. Items 610. Consider a water wave propagating along a straight line on a river, and has the following wave function: Hist) = ([10375m]cos((l45rad/cmx + 5.40rad/st) where y is the displacement at right angles to the surface of the river. 6. Determine the amount of time it will take for one complete wave pattern to pass a boatman aoat at anchor. 7. At which horizontal distance will the wave crest propagate at the time interval in Question 6? 8. Solve for the wave number. 9. Determine the number of waves per second that will have passed the boatman. 10. 10. Determine the speed with which the crest of the wave will travel past the boatm an. 13.3 Propagation of Waves on a String A. Identifyr whether each statement is true or false. If it is false, correct the underlined word or phrase. 1. In a transverse waveI a particle moves parallel to the direction with which the wave propagates. v,- Transverse impulse is equal to FT'. The transverse momentum is a product of the mass and the transverse acceleration. Wave speed is equal to the restoring force returning the system to equilibrium divided by the moment of inertia that resists the system to return to equilibrium. All wave motions are accompanied by mg} In a transverse wave. the portion of a string that moves has a mass m that is the product of p a d vi. The speed of a transverse wave on a string is determined by the spring force and linear mass density. . Power in waves refers to the spontaneous rate with which the energy is transmitted across the string at X and t. _ E The equation 1: _ J; is only applicable for mechanical waves on a taut or stretched string. 10. In a sinusoidal wave. the instantaneous power may be either positive or negative. B. Solve the following problems Items 14. The left end of a straight. horizontal rope is connected to one of the prongs of a metronome. which is oscillating the rope to produce transverse waves at 120 Hz. The right end droops over a pulley heavy with a 1.5kg mass. Suppose that the rope has a mass per unit length equal to 0.055 lggm. 1. Solve for the speed of the wave on the rope. 2. Determine the wavelength. 3. Determine the wave speed it the mass is increased to 3.0 kg. 4 . Calculate the new wavelength for Question 4. Items 57. Consider a rope of L : 98.43 in and m : 0.12 kg. Suppose it will be stretched such that transverse waves with f : 40 Hz will have a it. of 29.53 in. Express your answers in terms of their SI units. 5. What is the speed of the wave? 6. What is the rope's linear mass density? 7. With what tension mu st the rope be stretched to have a wavelength of 29.53 in? Items 8 10.A 0.0165kg wire of length 0.15 n1 has its left end tied to a pole, and the right end is wound on an adjustable screw that calibrates the tension upon the wire. Express your answers in terms of their 5] units. 8. Calculate the speed that this wave will have. 9. Determine the equation for the tension force in terms of the wave speed and the mass per unit length. 10. Which tension can produce a transverse wave of wavelength : 0.22 m and generates 625 oscillations every second? 13.4 Characteristics of Sound A. Identify what is being asked. Write the answer on the space provided before each number. 1. It is the physical quantity that measures the] oudness or softness of sound. It is the unit used to measure sound level. It is the frequency range below 20 Hz. It is the minimum sound intensity that is audible to the human ear. Threshold of hearing It refers to the frequency range above 20 000 Hz. It is the law governing the intensity of sound from a point source at a distance. It is the term used to describe the frequency range from 20 Hz to 20 000 Hz. These are the base units of frequency. omsowewe . It refers to the physical quantity that can help in the perception of pitch. frequency 10. These are the base units of intensity. 6. The sound intensity perceived from a point source is 0.50 Wlmz when at a distance of 5.0 In. What is the power output of the point source? 7. The intensity of a sound wave is 6.0 x 10 6 Wicmz . If you increase the sound level of the sound wave by 10 decibels, what is the new intensity? 8. Given that sound wave A has an intensity 100 times greater than sound wave B. what is the difference o_f the sound level between the two? 9. If you increase the sound level of a source by 10 dB, by what factor does the intensity increase? 10. A microphone can absorb 1.1 mW of sound on a surface area of 2.0 cmz . Calculate the intensity of the sound entering the microphone. 13. 7 Doppler Effect A. Identify what is being asked. Write the answer on the space provided before each number. 1. 91%er It is the change in the perceived frequency due to the relative motion of the source and the observer. The perceived frequency The perceived frequency The perceived frequency The perceived frequency when an observer moves toward a source. when the source moves away from an observer. when the source moves toward an observer. when an observer moves away from a source. B. Identify whether each statement is true or false. 1. 91er The Doppler effect occurs when the intensity of the sound changes as a source moves toward or away from a listener. As the source moves toward an observer, the wavelength becomes longer. Doppler effect can only occur if there is relative motion between an observer and a source. Doppler effect can also occur for other types of waves As an observer moves toward a stationary source. the wavelength of the source will decrease. Items 4-6. A girl is riding a car at a constant speed of 50 m/s and a stationary source of sound is being produced by a flute player. If the flute player produces a pitch of 440 Hz. 4. What will be the frequency perceived by the girl if she moves toward the flute player? 5. What will be the frequency perceived by the girl if she moves away from the flute player? 6. What is the total change in frequency heard by the girl as she passes toward then away from the flute player? Items 7-10. A thief riding a stolen car and moving at 45 m/s is being chased by a police car moving at 15 m/s. If the police car produces a sound from its siren at a frequency of 300 HZ, 7. What is the frequency being perceived by the car thief? 8. If instead, the car thief was the one producing the sound at 300 Hz from a loudspeaker, what is the frequency that the police officer hears from his police car? 9. If the police officer finally catches up to the car thief at 45 m/s, what would be the frequency perceived by the car thief? 10. If the car thief increases his velocity to 50 m/s while the police officer is at 45 m/s, what is now the perceived frequency of the car thief from the siren