Exam 14: Superposition and Standing Waves

A vertical tube one meter long is open at the top.It is filled with 75 cm of water.If the velocity of sound is 344 m/s,what will the fundamental resonant frequency be (in Hz)?

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 waves are described by y₁ = 6 cos 180t and y₂ = 6 cos 186t,(both in meters). With what angular frequency does the maximum amplitude of the resultant wave vary with time?

Two harmonic waves are described by $y _ { 1 } = ( 7 \mathrm {~m} ) \sin \left( \frac { 5 } { m } x - \frac { 100 } { s } t \right)$ $y _ { 2 } = ( 7 m ) \sin \left( \frac { 5 } { m } x - \frac { 100 } { s } t + 2 \right)$ What is the phase (in rad)of the resultant wave when x = t = 0?

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?

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x)cos 5t where x is in m and t is in s.What is the wavelength of the interfering waves?

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?

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?

The superposition of two waves $y _ { 1 } = ( 0.006 \mathrm {~cm} ) \cos \left[ 2 \pi \left( \frac { 156 } { \mathrm {~s} } t \right) \right]$ and $y _ { 2 } = ( 0.006 \mathrm {~cm} ) \cos \left[ 2 \pi \left( \frac { 150 } { \mathrm {~s} } t \right) \right]$ at the location x = 0 in space results in

A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x,t)= s_m cos (kx - $\omega$ t).Its velocity can be obtained from

Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0 *10 ^{- 3} kg/m and a tension of 80 N when both ends are fixed in place.

A stretched string is observed to vibrate in three equal segments when driven by a 480 Hz oscillator.What is the fundamental frequency of vibration for this string?

Two point sources emit sound waves of 1.0-m wavelength.The sources,2.0 m apart,as shown below,emit waves which are in phase with each other at the instant of emission.Where,along the line between the sources,are the waves out of phase with each other by $\pi$ radians?

Two organ pipes,a pipe of fundamental frequency 440 Hz,closed at one end,and a pipe of fundamental frequency 660 Hz,open at both ends,produce overtones.Which choice below correctly describes overtones present in both pipes?

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

As shown below,a garden room has three walls,a floor and a roof,but is open to the garden on one side.The wall widths are L and w.The roof height is h.When traveling sound waves enter the room,standing sound waves can be present in the room if the wavelength of the standing waves is

Which of the following wavelengths could NOT be present as a standing wave in a 2 m long organ pipe open at both ends?