Exam 16: Superposition and Standing Waves

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

A string with length L is fixed on both ends.If $\lambda$ _o = 2L and f_o = v/ $\lambda$ _o,the wave function for the harmonic shown is

Two whistles produce sounds with wavelengths 3.40 m and 3.30 m.What is the beat frequency produced? (the speed of sound is 340 m/s)

Two pipes closed at one end of length L₁ and L₂ are excited at their resonant frequencies.If the beat period is B_f Hz,then the velocity of sound is given by:

A vibrating tuning fork is held above a tube filled with water.The first two resonances occur when the water level is lowered by 14.2 cm and 44.2 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 the frequency of the tuning fork.Assume the speed of sound to be 330 m/s.

A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N.Resonant frequencies are found at 558 Hz and the next one at 744 Hz.What is the length of the wire?

If two identical waves with the same phase are added,the result is

In a vibrating-string experiment,three loops are observed between points A and B when the mass on one end of the string is 100 g.The number of loops between A and B can be changed to two by replacing the 100-g mass with a mass of

The standing waves in air in a pipe of length L that is open at both ends have a speed v.The frequencies of the three lowest harmonics are

When a piano tuner strikes both the A above middle C on the piano and a 440 Hz tuning fork,he hears 4 beats each second.The frequency of the piano's A is

Two waves with the same frequency and wavelength but with different amplitudes are added.If A₁ = 2A₂ and the waves are 180º out of phase,then the amplitude of the resultant wave is

A violinist is tuning the A string on her violin by listening for beats when this note is played simultaneously with a tuning fork of frequency 440 Hz.She hears a beat frequency of 4 Hz.She notices that,when she increases the tension in the string slightly,the beat frequency decreases.What was the frequency of the mistuned A string?

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 + $\pi$ /2).The amplitude resulting from the interference of the two waves is

A pipe produces successive harmonics at 300 Hz and 350 Hz.Calculate the length of the pipe and state whether it is closed at one end or not.Assume the speed of sound to be 340 m/s.

The fundamental frequency of a pipe that has one end closed is 256 Hz.When both ends of the same pipe are opened,the fundamental frequency is

In a pipe that is open at one end and closed at the other and that has a fundamental frequency of 256 Hz,which of the following frequencies cannot be produced?

A vibrating tuning fork of 725 Hz is held above a tube filled with water.Successive resonances are heard when the water level is lowered by 11.5 cm and 34.5 cm from the top of the tube.Calculate a value for the speed of sound.(Hint: remember the small end correction $\Delta$ L at the top of the tube.)

What is the third harmonic of an open-both-ends organ pipe of length 1.5 m? Assume the speed of sound to be 340 m/s.

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 speed of a transverse wave in the string is

The human vocal tract can be thought of as a tube that is open at one end.If the length of this tube is 17 cm (about average for an adult male),what are the lowest two harmonics?