Exam 14: Superposition and Standing Waves

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?

Two harmonic waves are described by $y _ { 1 } = ( 6.00 \mathrm {~cm} ) \sin \left( \pi \left( \frac { 2.00 } { \mathrm {~m} } x + \frac { 3.00 } { \mathrm {~s} } t \right) \right)$ $y _ { 2 } = ( 6.00 \mathrm {~cm} ) \sin \left( \pi \left( \frac { 2.00 } { \mathrm {~m} } x - \frac { 3.00 } { \mathrm {~s} } t \right) \right)$ What is the magnitude of the displacement (in cm)of this wave at x = 3 cm and t = 5 sec?

Which of the following frequencies could NOT be present as a standing wave in a 2m long organ pipe open at both ends? The fundamental frequency is 85 Hz.

Two waves are described by y₁ = 6 cos 180t and y₂ = 6 cos 186t,(both in meters). What effective frequency does the resultant vibration have at a point?

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (4x)cos (3t)where x is in m and t is in s.What is the speed (in m/s)of the interfering waves?

The superposition of two waves, $y _ { 1 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t \right) \right]$ and $y _ { 2 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t - \frac { 1 } { 2 } \right) \right]$ , results in a wave with a frequency of

Two ropes are spliced together as shown. A short time after the incident pulse shown in the diagram reaches the splice,the rope's appearance will be that in

Two harmonic waves are described by $y _ { 1 } = ( 3 \mathrm {~m} ) \sin \left( \frac { 4 } { m } x - \frac { 700 } { s } t \right)$ $y _ { 2 } = ( 3 m ) \sin \left( \frac { 4 } { m } x - \frac { 700 } { s } t - 2 \right)$ What is the amplitude of the resultant wave?

A length of organ pipe is closed at one end.If the speed of sound is 344 m/s,what length of pipe (in cm)is needed to obtain a fundamental frequency of 50 Hz?

An organ pipe open at both ends has a radius of 4.0 cm and a length of 6.0 m.What is the frequency (in Hz)of the third harmonic? (Assume the velocity of sound is 344 m/s. )

The superposition of two waves, $y _ { 1 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t \right) \right]$ and $y _ { 2 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t - \frac { 1 } { 2 } \right) \right]$ , results in a wave with a phase angle of

Which of the following wavelengths could NOT be present as a harmonic on a 2 m long string?

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 wavelength (in cm)of the first harmonic?

Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond. Use this exhibit to answer the following question. -Refer to Exhibit 18-1.The phase difference in radians between points A and D is

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams.To what tension must this wire be stretched to make the fundamental frequency correspond to middle C,(f_c = 261.6 Hz)?

Two harmonic waves are described by $y _ { 1 } = ( 5 \mathrm {~m} ) \sin \left( \frac { 6 } { \mathrm {~m} } x - \frac { 900 } { \mathrm {~s} } t \right)$ $y _ { 2 } = ( 5 \mathrm {~m} ) \sin \left( \frac { 6 } { m } x - \frac { 900 } { \mathrm {~s} } t - 2 \right)$ What is the wavelength of the resultant wave?

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?

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency.At the time,the speed of sound in air is 340 m/s.How many beats per second do the people on the fire engine hear?

When two organ pipes open at both ends sound a perfect fifth,such as two notes with fundamental frequencies at 440 Hz and 660 Hz,both pipes produce overtones.Which choice below correctly describes overtones present in both pipes?

Two pulses are traveling towards each other at 10 cm/s on a long string at t = 0 s,as shown below. Which diagram below correctly shows the shape of the string at 0.5 s?