Question 1

Two harmonic waves are described by   What is the frequency (in Hz) of the resultant wave?
A)300
B)48
C)8
D)0.8
E)150

Accepted Answer

B

Question 2

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)1000
E)200

Accepted Answer

B

Question 3

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)3
B)0.25
C)0
D)6
E)1.5

Accepted Answer

C

Question 4

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 third harmonic of an organ pipe open at both ends corresponds to three antinodes (points of maximum displacement) along the length of the pipe. The wavelength of this harmonic will be twice the length of the pipe, or 12.0 m. Using the equation:
velocity = frequency x wavelength 
we can solve for the frequency:
frequency = velocity / wavelength = 344 m/s / 12.0 m = 28.7 Hz (rounded to the nearest tenth)
However, since the question asks for the frequency to the nearest whole number, we need to round up to 29 Hz. Therefore, the correct answer choice is B) 86.

Question 5

Two instruments produce a beat frequency of 5 Hz. If one has a frequency of 264 Hz, what could be the frequency of the other instrument?
A)269 Hz
B)254 Hz
C)264 Hz
D)5 Hz
E)274 Hz

Accepted Answer

The answer of Two instruments produce a beat frequency of...

Question 6

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

Accepted Answer

The distance between the first two antinodes in a standing wave is equal to half the wavelength. The given equation is $y = 2 \sin (\pi x) \cos (3\pi t)$. The spatial part of the wave equation, $\sin (\pi x)$, determines the pattern of nodes and antinodes. The wavelength $\lambda$ can be found from the spatial part's coefficient of $x$, which is $\pi$. Since the general form for a wave is $\sin(kx)$ where $k = \frac{2\pi}{\lambda}$, comparing it to $\sin(\pi x)$ gives $k = \pi = \frac{2\pi}{\lambda}$, solving for $\lambda$ gives $\lambda = 2$ meters. Therefore, the distance between the first two antinodes, which is half the wavelength, is $1$ meter.

Question 7

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?
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 8

Two harmonic waves are described by   What is the magnitude of the speed (in m/s) of the two traveling waves?
A)16
B)4.0
C)8.0
D)0.25
E)2.0

Accepted Answer

The answer of Two harmonic waves are described by ...

Question 9

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?
A)28
B)86
C)344
D)172
E)688

Accepted Answer

The formula to find the wavelength of the fundamental frequency of an organ pipe closed at one end is:

wavelength = 4 * length / 3

We know the speed of sound is 344 m/s and the frequency is 50 Hz. We can use the formula:

wavelength = speed / frequency

wavelength = 344 / 50 = 6.88 m

Now we can solve for the length of the pipe:

6.88 = 4 * length / 3
3 * 6.88 = 4 * length
length = 3 * 6.88 / 4 = 5.16 m

Convert to centimeters:

length = 5.16 * 100 = 516 cm

The closest answer is D) 172 cm.

Question 10

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...

Question 11

Two harmonic waves are described by   What is the phase (in rad) of the resultant wave when x = t = 0?
A)3
B)0
C)2
D)1
E)4

Accepted Answer

The answer of Two harmonic waves are described by ...

Question 12

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)90
B)400
C)1.57
D)7.85
E)15

Accepted Answer

The phase difference is calculated using the formula $\Delta \phi = \frac{2\pi}{\lambda} \Delta x$, where $\Delta x$ is the path difference and $\lambda$ is the wavelength. Substituting the given values, $\Delta \phi = \frac{2\pi}{4} \times 5 = \frac{5\pi}{2}$ radians. Converting to degrees, $\frac{5\pi}{2} \times \frac{180}{\pi} = 450$ degrees. Since phase differences are typically expressed in the range of 0 to 360 degrees, we subtract 360 degrees to get 90 degrees.

Question 13

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

A tube closed at one end has odd harmonics as its resonant frequencies (i.e., only odd multiples of the fundamental frequency are allowed). The fundamental frequency is given by the equation: f1 = v/4L, where v is the velocity of sound (344 m/s) and L is the length of the tube (1.0 m). So, f1 = 86 Hz.

Question 14

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

A string vibrating in three equal segments produces three nodes and two antinodes. This is the second harmonic (first overtone) of the string, which has a frequency that is twice the fundamental frequency. Therefore, the fundamental frequency is 480 Hz / 2 = 240 Hz.

Question 15

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3sin(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 given by y = 3sin(2x)cos(5t) is the result of the interference of two waves traveling in opposite directions. We can see that the wave function consists of a product of two terms: sin(2x) and cos(5t). The sin(2x) term represents a wave with a wavelength of 2π/2 = π m, since the coefficient of x is 2. Similarly, the cos(5t) term represents a wave with a period of 2π/5 s, and therefore a wavelength of λ = vt = (2π/5)(1/2) = π/5 m.

Since a standing wave is the result of the interference of two waves traveling in opposite directions, the wavelength of the interfering waves must be twice the wavelength of the standing wave. Therefore, the wavelength of the interfering waves is 2π = 6.28 m. However, this is not one of the answer choices. The closest answer choice is A) 3.14 m, which is half of the wavelength of the interfering waves. This is the correct answer, since the standing wave is the result of the interference of two waves traveling in opposite directions, and the distance between successive nodes of the standing wave is equal to half the wavelength of the interfering waves.

Question 16

Two harmonic waves are described by   What is the amplitude of the resultant wave?
A)8.0 m
B)4.3 m
C)6.0 m
D)3.2 m
E)3.0 m

Accepted Answer

The answer of Two harmonic waves are described by ...

Question 17

Two harmonic waves are described by   What is the wavelength of the resultant wave?
A)3 m
B)2 m
C)1 m
D)4 m
E)6 m

Accepted Answer

To find the wavelength of the resultant wave, we need to find the difference between the wavelengths of the two waves.

Wave 1: 11eb8c7e_f5a2_3c23_8371_d764800df84f_TB8847_11 (wavelength = 2m)
Wave 2: 11eb8c7e_f5a2_3c24_8371_e1ebffc1e905_TB8847_11 (wavelength = 3m)

Difference = 3m - 2m = 1m

Therefore, the wavelength of the resultant wave is 1m, which is answer choice C.

Question 18

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 of a string fixed at both ends can be calculated using the formula:
f = (1/2L) * sqrt(Tension/linear density)
where L is the length of the string, Tension is the tension in the string, and linear density is the density per unit length of the string.

Substituting the given values, we get:
f = (1/2*200) * sqrt(600/0.015) 
f = 158 Hz

Therefore, the answer is C.

Question 19

Two tuning forks with frequencies 264 and 262 Hz produce "beats". What is the beat frequency (in Hz)?
A)4
B)2
C)1
D)3
E)0 (no beats are produced)

Accepted Answer

The beat frequency is the absolute difference between the two frequencies, which is |264 Hz - 262 Hz| = 2 Hz.

Question 20

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2sin(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 $v = \frac{3}{4} = 0.75 \, \text{m/s}$.

Quiz 18: Superposition and Standing Waves

Two harmonic waves are described by What is the frequency (in Hz) 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 wavelength (in cm) of the first harmonic?

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.

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.)

Two instruments produce a beat frequency of 5 Hz. If one has a frequency of 264 Hz, what could be the frequency of the other instrument?

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?

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?

Two harmonic waves are described by What is the magnitude of the speed (in m/s) of the two traveling waves?

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?

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) ?

Two harmonic waves are described by What is the phase (in rad) of the resultant wave when x = t = 0?

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

Two harmonic waves are described by What is the amplitude of the resultant wave?

Two harmonic waves are described by 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?

Two tuning forks with frequencies 264 and 262 Hz produce "beats". What is the beat frequency (in Hz) ?

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

Quiz 18: Superposition and Standing Waves

Two harmonic waves are described by What is the frequency (in Hz) 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 wavelength (in cm) of the first harmonic?

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.

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.)

Two instruments produce a beat frequency of 5 Hz. If one has a frequency of 264 Hz, what could be the frequency of the other instrument?

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?

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?

Two harmonic waves are described by What is the magnitude of the speed (in m/s) of the two traveling waves?

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?

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) ?

Two harmonic waves are described by What is the phase (in rad) of the resultant wave when x = t = 0?

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

Two harmonic waves are described by What is the amplitude of the resultant wave?

Two harmonic waves are described by 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?

Two tuning forks with frequencies 264 and 262 Hz produce "beats". What is the beat frequency (in Hz) ?

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

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