Question 1

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 4 sin (5x)cos (6t)where x is in m and t is in s.What is the approximate frequency of the interfering waves?
A)3 Hz
B)1 Hz
C)6 Hz
D)12 Hz
E)5 Hz

Accepted Answer

The answer of Two harmonic waves traveling in opposite directions...

Question 2

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?
A)0.800,0.670,0.500
B)1.33,1.00,0.500
C)2.00,1.00,0.500
D)2.00,1.33,1.00
E)4.00,2.00,1.00

Accepted Answer

The wavelengths of the harmonics present on both strings must be the same. The fundamental mode for the 1.00 m string has a wavelength of 2.00 m, and the fundamental mode for the 2.00 m string has a wavelength of 4.00 m. Therefore, any common harmonics must have wavelengths that are integer divisors of both 2.00 m and 4.00 m. The only common divisors are 2.00 m and 1.00 m, so the harmonics must have wavelengths of 2.00 m, 1.00 m, or 0.500 m. The only choice that includes all three of these options is C.

Question 3

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?
A)0.75
B)0.25
C)1.3
D)12
E)3.0

Accepted Answer

The speed of the waves can be determined from the wave equation. The general form of a standing wave resulting from the interference of two waves traveling in opposite directions can be given by $y = 2A \sin(kx) \cos(\omega t)$, where $k$ is the wave number and $\omega$ is the angular frequency. The speed $v$ of the waves can be found using the relationship $v = \frac{\omega}{k}$. Given $k = 4 \, \text{m}^{-1}$ and $\omega = 3 \, \text{s}^{-1}$, the speed $v = \frac{3}{4} = 0.75 \, \text{m/s}$.

Question 4

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?
A)480 Hz
B)320 Hz
C)160 Hz
D)640 Hz
E)240 Hz

Accepted Answer

If the string is vibrating in three equal segments, it means there are two nodes dividing the string into three segments. This is the third harmonic, which means there are three wavelengths (cycles) of vibration in the length of the string. Therefore, the fundamental frequency (first harmonic) would be three times lower than the third harmonic frequency, which is:
480 Hz / 3 = 160 Hz (Choice C)

Question 5

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. )
A)76
B)86
C)54
D)28
E)129

Accepted Answer

The answer of An organ pipe open at both ends...

Question 6

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)30 N
B)45 N
C)80 N
D)8.9 N
E)13 N

Accepted Answer

The number of antinodes in a resonant standing wave on a string is directly proportional to the tension in the string. 
From the given information, when the tension is 20 N, there are 3 antinodes in the standing wave. 
To find the tension required for 2 antinodes, we can use the following proportionality: 
tension 1 / tension 2 = antinode 1 / antinode 2

Plugging in the values we have: 
20 / tension 2 = 3 / 2

Cross multiplying and solving for tension 2: 
tension 2 = 40 / 3 = 13.3 N (approximately)

The closest answer choice to 13.3 N is B, 45 N.

Question 7

Two identical strings have the same length and same mass per unit length.String B is stretched with four times as great a tension as that applied to string A.Which statement is correct for all n harmonics on the two strings,n = 1,2,3...? A) $f _ { \mathrm { nb } } = \frac { 1 } { 4 } f _ { \mathrm { nA } }$ . B) $f _ { \mathrm { nb } } = \frac { 1 } { 2 } f _ { \mathrm { nA } }$ . C) $f _ { n , B } = \sqrt { 2 } f _ { n , A }$ . D)f_n,B = 2f_n,A. E)f_n,B = 4f_n,A.

Accepted Answer

The frequency of a harmonic on a string is proportional to the square root of the tension. Since string B has four times the tension of string A, the frequency of the nth harmonic on string B will be twice that of the nth harmonic on string A.

Question 8

A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator.Which of the following can be changed by changing the frequency of the oscillator?
A)The speed of the waves traveling along the string.
B)The tension in the string.
C)The wavelength of the waves on the string.
D)All of the above.
E)None of the above.

Accepted Answer

The frequency of the oscillator is directly proportional to the frequency of the waves on the string, which determines the wavelength according to the equation λ = v/f, where λ is the wavelength, v is the speed of the waves, and f is the frequency. Therefore, changing the frequency of the oscillator will change the wavelength of the waves on the string, but it will not change the speed of the waves or the tension in the string.

Question 9

In a standing wave,not necessarily at the fundamental frequency,on a string of length L,the distance between nodes is
A)$\lambda$/4.
B)$\lambda$/2.
C)$\lambda$.
D)L/4.
E)L/2.

Accepted Answer

The distance between nodes in a standing wave on a string of length L can be found using the formula d = λ/2, where d is the distance between nodes and λ is the wavelength of the wave. At any frequency other than the fundamental frequency, the wavelength will be shorter than the length of the string, so the distance between nodes will be less than L. Therefore, the only option that satisfies this condition is B, which gives d = λ/2.

Question 10

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?
A)600
B)400
C)800
D)1 000
E)200

Accepted Answer

The answer of A string is stretched and fixed at...

Question 11

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)316 Hz
B)632 Hz
C)158 Hz
D)215 Hz
E)79 Hz

Accepted Answer

The fundamental frequency (f) of a string fixed at both ends can be found using the equation f = (1/2L)×√(T/μ), where L is the length of the string, T is the tension, and μ is the linear density (mass per unit length). 
Substituting the given values, f = (1/2×200 cm)×√(600 N/0.015 g/cm) = 158 Hz. Therefore, the best choice is C.

Question 12

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)?
A)264
B)140
C)86
D)440
E)172

Accepted Answer

The fundamental frequency of a tube closed at one end can be calculated using the formula f = V/4L, where V is the velocity of sound and L is the length of the tube. 
Substituting the given values, we get f = 344/4*1.0 = 86 Hz. 
Therefore, the correct answer is choice C, 86.

Question 13

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?
A)12.0
B)3.00
C)6.00
D)2.25
E)0

Accepted Answer

The answer of Two harmonic waves are described by \[y...

Question 14

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?
A)3.14 m
B)1.00 m
C)6.28 m
D)12.0 m
E)2.00 m

Accepted Answer

The standing wave is described by the equation:

y = 3 sin(2x) cos(5t)

We can see that the spatial part of this equation is y = 3 sin(2x), which represents a harmonic wave with a wavelength of:

λ = 2π/k = 2π/2 = π

Therefore, the wavelength of the interfering waves is half of this value, or:

λ/2 = π/2 = 3.14 m

So the correct answer is A) 3.14 m.

Question 15

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?
A)8
B)2
C)4
D)1
E)0.5

Accepted Answer

The answer of Two harmonic waves traveling in opposite directions...

Question 16

Two harmonic waves are described by $y _ { 1 } = ( 6 \mathrm {~cm} ) \sin \left( \pi \left( \frac { 8 } { \mathrm {~m} } x + \frac { 2 } { \mathrm {~s} } t \right) \right)$
$$y _ { 2 } = ( 6 \mathrm {~cm} ) \sin \left( \pi \left( \frac { 8 } { \mathrm {~m} } x - \frac { 2 } { \mathrm {~s} } t \right) \right)$$ From the choices given,determine the smallest positive value of x (in cm)corresponding to a node of the resultant standing wave.
A)3
B)0.25
C)0
D)6
E)1.5

Accepted Answer

The answer of Two harmonic waves are described by \(y...

Question 17

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? A)3 B)4,since all resonances in this situation have the same number of nodes C)5 D)2,since resonances only involve whole wavelengths E)6,since resonances only involve whole wavelength

Accepted Answer

The answer of A string with a fixed frequency vibrator...

Question 18

Which of the following wavelengths could NOT be present as a harmonic on a 2 m long string?
A)4 m
B)2 m
C)1 m
D)0.89 m
E)0.5 m

Accepted Answer

The harmonic wavelengths that can exist on a 2m long string can be found using the formula: λ = 2L/n where L is the length of the string and n is the harmonic number (1, 2, 3, ...). Plugging in L=2m, we get:
n=1: λ=4m
n=2: λ=2m
n=3: λ=4/3m
n=4: λ=1m
n=5: λ=4/5m
...
The wavelengths can only be multiples of the fundamental wavelength (n=1), so any non-multiple value cannot exist. Therefore, the wavelength of 0.89 m is not a valid harmonic on a 2m long string.

Question 19

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 
A) $\frac { 2 L } { n }$ ,where n is a positive integer.
B) $\frac { 4 w } { n }$ ,where n is an odd integer.
C) $\frac { h } { n }$ ,where n is an even integer.
D)in all cases listed above.
E)given by (a)or (b)above,but not by (c).

Accepted Answer

The answer of As shown below,a garden room has three...

Question 20

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)3.4
B)172
C)344
D)1.7
E)688

Accepted Answer

The answer of A vertical tube one meter long is...

Quiz 14: Superposition and Standing Waves

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

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?

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?

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. )

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 identical strings have the same length and same mass per unit length.String B is stretched with four times as great a tension as that applied to string A.Which statement is correct for all n harmonics on the two strings,n = 1,2,3...?

A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator.Which of the following can be changed by changing the frequency of the oscillator?

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

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?

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 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) ?

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 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?

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

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) ?