Exam 16: Superposition and Standing Waves

A string 2.0 m long has a mass of 2.4 $\times$ 10^-2 kg.When fixed at both ends,it vibrates with a fundamental frequency of 150 Hz.The frequency of the third harmonic of this fundamental is

Use the figure below to answer the next problem. The graph shows a wave pulse of width w = 5 cm and speed v = 100 m / s. -The duration of the wave pulse is

What is the phase difference at any given instant between two points on a wave which are 1.52 m apart if the wavelength of the wave is 2.13 m?

A standing wave is shown in the figure on the right.If the period of the wave is T,the shortest time it takes for the wave to go from the solid curve to the dashed curve is

The fundamental frequency of a vibrating string is f₁.If the tension in the string is decreased by 50% while the linear density is held constant,the fundamental frequency becomes

The figure shows a standing wave in a pipe that is closed at one end.The frequency associated with this wave pattern is called the

A guitar string of length 105 cm is in resonance with a tuning fork of frequency f.Using the fret board the length of the string is shortened by 1.5 cm while keeping the tension in the string constant.Now a beat frequency of 10 Hz is heard between the string and the tuning fork.What is the frequency of the tuning fork?

A vibrating tuning fork of 850 Hz is held above a tube filled with water.The first and third resonances occur when the water level is lowered by 8.8 cm and 47.6 cm from the top of the tube.If there is a small end correction that adds a small extra length $\Delta$ L to the effective length of the air column,calculate $\Delta$ L.Assume the speed of sound to be 330 m/s.

If two identical waves with a phase difference of 6 $\pi$ are added,the result is

A string fixed at both ends is 50.0 cm long and has a tension that causes the frequency of its fundamental to be 262 Hz.If the tension is increased by 4%,what does the fundamental frequency become?

The third harmonic of a tube closed at one end is 735 Hz.If the speed of sound in air is 335 m/s,the length of the tube must be

A standing wave is created by oscillating a taut string at a frequency that corresponds to one of the resonant frequencies.The amplitude of the antinodes is very much larger than the amplitude of the oscillator.Does this violate the conservation of energy principle? Explain why.

When an organ pipe,which is closed at one end only,vibrates with a frequency that is three times its fundamental (first harmonic)frequency,

Two sound waves,one wave is given by y₁ = p_o sin (kx - $\omega$ t)and the other by y₂ = p_o sin (kx - $\omega$ t + $\pi$ /4).The phase constant resulting from the interference of the two waves is

A microphone is placed at the node of a standing sound wave.What does the microphone pick up?

The standing waves in air in a pipe of length L that is open at one end and closed at the other have a speed v.The frequencies of the three lowest harmonics are

On a standing-wave pattern,the distance between two consecutive nodes is d.The wavelength is

Two tones of equal amplitude but slightly different frequencies are emitted by a sound source.This gives rise to

A clarinet,which is essentially a tube that is open at one end,is properly tuned to concert A (440 Hz)indoors,where the temperature is 20ºC and the speed of sound is 340 m/s.The musician then takes the instrument to play an outdoor concert,where the temperature is 0ºC and the speed of sound is 331 m/s.What is the frequency of the A played on the cold clarinet? (Ignore any thermal changes in the body of the clarinet itself.)

A wire of mass 1.1 g is under a tension of 100 N.If its third overtone is at a frequency of 750 Hz,calculate the length of the wire.