Exam 16: Superposition and Standing Waves

Which of the following is an accurate statement?

Two harmonic waves of the same frequency and phase but of different amplitudes move in opposite directions on a string.A periodic series of maxima and minima on the string are observed.What is the ratio of the maximum displacement at a minimum position to that at a maximum position,if one amplitude is 52% of the other? (This is called the standing wave ratio. )

A simple harmonic wave described by the equation y(t)= 0.54 cos(3.1x - 2.3t)reflects from both ends of a string that is clamped at each end,resulting in a standing wave that is the sum of y(t)and its reflection.What is the amplitude of the standing wave at x = 0.22 m? The quantities x and y are in meters,and t is in seconds.

A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 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? (c)What other frequencies will this string allow?

Two speakers next to each other oscillate in phase,one at 404 Hz and the other at 400 Hz.If you stand in front of them,you will hear a sound of frequency 402 Hz that fluctuates between loud and soft with a frequency of 4 Hz.

A string,0.26 m long,vibrating in the n = 6 harmonic,excites an open pipe,0.88 m long,into second overtone resonance.The speed of sound in air is 345 m/s.The common resonant frequency of the string and the pipe,in SI units,is closest to:

The sound from two loudspeakers is received by a microphone at a point far away along the line through the speakers.The microphone registers maximum intensity when the speakers are 20 cm apart.The sound intensity decreases as the distance between the speakers is increased,reaching zero at a separation of 91 cm.If the distance between the speakers continues to increase,at what separation will the sound intensity again be a maximum?

A 2.0 g string,0.67 m long,is under tension.The string produces a 700 Hz tone when it vibrates in the third harmonic.The speed of sound in air is 344 m/s.The wavelength of the tone in air,in SI units,is closest to:

A thin film of refractive index 1.40 covers a flat sheet of glass of refractive index 1.50.If light of wavelength 600 nm strikes the film from air perpendicular to its surface,the minimum film thickness needed to cause destructive interference in the reflected light is 150 nm.

A violin with string length 32 cm and string density 1.5 g/cm resonates with the first overtone of an organ pipe with one end closed.The pipe length is 2 m.What is the tension in the string?

A 0.588 m string is clamped at both ends.If the lowest standing wave frequency in the string is 326 Hz,what is the wave speed?

To demonstrate interference of sound waves,a buzzer is placed in the center of an empty mailing tube that is 0.80 m long.The sound waves emerge from the two ends of the tube in phase and interfere with each other in the region surrounding the tube.When you stand 4.0 m directly in front of the tube,equidistant from its two ends,you hear a loud sound.If you then move parallel to the tube a distance of 1.3 m,the sound nearly disappears. (a)What's the wavelength of the buzzer's sound waves? (b)What's the buzzer's frequency? (Assume the speed of sound in air is 340 m/s. )

If the frequency of a violin string is to be increased by 20%,what change in tension must be applied?

Radio station KBOB broadcasts at a frequency of 85.7 MHz on your dial.Since nearly all 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 at exactly the same frequency,aligned on an east-west axis.For engineering reasons,the two towers must be at least 10 meters apart.What's the shortest distance between the towers that will eliminate all broadcast power to the east and west?

An open organ pipe is tuned to a given frequency.A second pipe with both ends open resonates with twice this frequency.What is the ratio of the length of the first pipe to the second pipe?

Current in a wire is reflected from an unconnected end (to ground)in the same way that sound reflects from an open pipe.If a 500.0 cm wire is excited by a 22.0 MHz oscillator in its lowest mode,what is the ratio of the current speed to that of light?

Two stereo speakers mounted 4.52 m apart on a wall emit identical sound waves.You are standing at the opposite wall of the room at a point directly between the two speakers.You walk 2.11 m parallel to the wall,to a location where you first notice that the sound intensity is much less.If the wall along which you are walking is 10.7 m from the wall with the speakers,what is the wavelength of the sound waves?

The tension in each of two strings is adjusted so that both vibrate at exactly 666 Hz.The tension in one of the strings is then increased slightly.As a result,six beats per second are heard when both strings vibrate.What is the new frequency of the string that was tightened?

A 500.0 cm rope under a tension of 70.0 N.is set into oscillation.The mass density of the rope is 120.0 g/cm.What is the frequency of the first harmonic mode (m = 2)?

Two motors in a factory are running at slightly different rates.One runs at 825 rpm and the other at 786 rpm.You hear the sound intensity increase and then decrease periodically due to wave interference.How long does it take between successive instances of the sound intensity increasing?