Exam 14: Periodic Motion

Standing waves on a string: A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN. What is the frequency of the fundamental mode of vibration of this wire?

Sound level: A certain crying baby emits sound with an intensity of 8.0 × 10^-8 W/m². What is the intensity level due to a set of five such crying babies, all crying with the same intensity? You can neglect any absorption, reflection, or interference of the sound. The lowest detectable intensity is 1.0 × 10^-12 W/m².

Interference: Two identical loudspeakers that are 5.00 m apart and face toward each other are driven in phase by the same oscillator at a frequency of 875 Hz. The speed of sound in the room is 344 m/s. If you start out standing midway between the speakers, find the shortest distance you can walk toward either speaker in order to hear a minimum of sound.

Interference: Radio station KBOB broadcasts at a frequency of 85.7 MHz on your dial using radio waves that travel at 3.00 × 10⁸ m/s. Since most of the station's audience is due south of the transmitter, the managers of KBOB don't want to waste any energy broadcasting to the east and west. They decide to build two towers, transmitting in phase at exactly the same frequency, aligned on an east-west axis. For engineering reasons, the two towers must be AT LEAST 10.0 m apart. What is the shortest distance between the towers that will eliminate all broadcast power to the east and west?

Doppler effect: A woman is riding a bicycle at 7.80 m/s along a straight road that runs parallel to and right next to some railroad tracks. She hears the whistle of a train that is behind. The frequency emitted by the train is 840 Hz, but the frequency the woman hears is 778 Hz. Take the speed of sound to be 340 m/s. (a) What is the speed of the train, and is the train traveling away from or toward the bicycle? (b) What frequency is heard by a stationary observer located between the train and the bicycle?

Waves on a string: When a weight W is hanging from a light vertical string, the speed of pulses on the string is V. If a second weight W is added without stretching the string, the speed of pulses on this string will now become

Standing waves on a string: A guitar string 0.650 m long has a tension of 61.0 N and a mass per unit length of 3.00 g/m. (a) What is the speed of waves on the string when it is plucked? (b) What is the string's fundamental frequency of vibration when plucked?

Speed of sound: The density of aluminum is 2.7 × 10³ kg/m³. The speed of longitudinal waves in an aluminum rod is measured to be 5.1 × 10³ m/s. What is the value of Young's modulus for this aluminum?

Standing waves on a string: A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension. This string produces a 100-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in is closest to

Standing waves on a string: A 2.0-m string is fixed at both ends and tightened until the wave speed is What is the frequency of the standing wave shown in the figure?

Standing sound waves: A tube open at one end and closed at the other end produces sound having a fundamental frequency of 350 Hz. If you now open the closed end, the fundamental frequency becomes

Doppler effect: You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1370 Hz. You are relieved that he is in pursuit of a different speeder when he continues past you, but now you perceive the frequency as 1330 Hz. What is the speed of the police car? The speed of sound in air is 343 m/s.

Doppler effect: A stationary siren emits sound of frequency 1000 Hz and wavelength 0.343 m. An observer who is moving toward the siren will measure a frequency f and wavelength λ for this sound such that

Standing sound waves: A string 40.0 cm long of mass 8.50 g is fixed at both ends and is under a tension of 425 N. When this string is vibrating in its third OVERTONE, you observe that it causes a nearby pipe, open at both ends, to resonate in its third HARMONIC. The speed of sound in the room is 344 m/s. (a) How long is the pipe? (b) What is the fundamental frequency of the pipe?

Speed of sound: A pipe that is 20.0 m long and 10.0 cm in diameter contains olive oil. The density of the olive oil is 890 kg/m³ and the bulk modulus is 1.3 × 10⁹ Pa. A 3.4-Hz longitudinal wave is transmitted in the oil. How many milliseconds does it take for the wave to travel the length of the pipe in the oil?

Standing waves on a string: A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N. If it is set into small-amplitude oscillation, what is the frequency of the first harmonic mode?

Doppler effect: A plane flies toward a stationary siren at 1/4 the speed of sound. Then the plane stands still on the ground and the siren is driven toward it at 1/4 the speed of sound. In both cases, a person sitting in the plane will hear the same frequency of sound from the siren.

Interference: Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 8.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 3.00 m parallel to the wall, she experiences destructive interference for the second time. What is the frequency of the sound? The speed of sound in the room is 343 m/s. CAREFUL! The distance to the wall is NOT much greater than the distance between the speakers.

Mathematics of traveling waves: Ocean tides are waves that have a period of 12 hours, an amplitude (in some places) of 1.50 m, and a speed of 750 km/hr. What is the distance between adjacent crests of these waves?

Speed of sound: The speed of sound in an alcohol at a temperature of 20°C is 1260 m/s. The density of the alcohol at that temperature is At a temperature of 20°C, find the bulk modulus of the alcohol.