Exam 18: Superposition and Standing Waves

A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the fundamental frequency?

The superposition of two waves, and , results in a wave with a wavelength of

Two waves are described by ​ Y1 = 6cos(180t) and y2 = 6cos(186t) (both in meters). ​ With what angular frequency does the maximum amplitude of the resultant wave vary with time?

An observer stands 3 m from speaker A and 4 m from speaker B. Both speakers, oscillating in phase, produce 170-Hz waves. The speed of sound in air is 340 m/s. What is the phase difference (in radians) between the waves from A and B at the observer's location, point P? ​ ​

Tuning forks #1, #2, and #3 each have slightly different frequencies.When #1 and #2 are sounded together, a beat frequency of 3 Hz results. When #2 and #3 are sounded together, a beat frequency of 5 Hz results. If the frequency of #1 is 100 Hz, which of the following cannot be the frequency of #3?

The superposition of two waves ​ and ​ At the location x = 0 in space results in

A string with a fixed frequency vibrator at one end is subjected to varying tensions. When the tension is 20 N, a resonance with 3 antinodes results. What tension would cause a resonance with 2 antinodes in this string?

A clarinet behaves like a tube closed at one end. If its length is 1.0 m, and the velocity of sound is 344 m/s, what is its fundamental frequency (in Hz)?

An organ pipe open at both ends is 1.5 m long. A second organ pipe that is closed at one end and open at the other is 0.75 m long. The speed of sound in the room is 330 m/s. Which of the following sets of frequencies consists of frequencies which can be produced by both pipes?

Two harmonic waves are described by From the choices given, determine the smallest positive value of x (in cm) corresponding to a node of the resultant standing wave.

A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x, t) = smcos(kx − ωt). Its velocity can be obtained from

In a standing wave, not necessarily at the fundamental frequency, on a string of length L, the distance between nodes is

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2sin(πx)cos(3πt), where x is in m and t is in s. What is the distance (in m) between the first two antinodes?

The figure below shows the positions of particles in a longitudinal standing wave. One quarter period later the particle distribution is shown in

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 4sin(5x)cos(6t) where x is in m and t is in s. What is the approximate frequency of the interfering waves?

The path difference between two waves is 5 m. If the wavelength of the waves emitted by the two sources is 4 m, what is the phase difference (in degrees)?

A string with a fixed frequency vibrator at one end is undergoing resonance with 4 antinodes when under tension T1. When the tension is slowly increased the resonance condition disappears until tension T2 is reached, there being no resonances occurring between these two tensions. How many antinodes are there in this new resonance?

Two strings are, respectively, 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?

Drummers like to have high-pitched cymbals that vibrate at high frequencies. To obtain the highest frequencies, a cymbal of a fixed size should be made of a material

A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. The wave speed is 540 m/s. What is the minimum frequency she should apply to set up standing waves?