Question 1

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 2

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 3

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

C

Question 4

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 5

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 6

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 7

Two harmonic waves are described by   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 ...

Question 8

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (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 9

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 wavelength is given by lambda = 2*pi/k, where k is the wave number. The wave number is given by k = 2*pi/lambda. So, lambda = 2*pi/k = 2*pi/(2*pi/3) = 3 m.

Question 10

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 11

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 12

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 13

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 14

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 fundamental frequency for a closed organ pipe is given by:

f = v/4L

where v is the speed of sound and L is the length of the pipe.

Rearranging the formula to solve for L yields:

L = v/4f

Substituting in the given values:

L = 344 m/s / 4(50 Hz) = 0.43 m = 43 cm

Therefore, the length of pipe needed to obtain a fundamental frequency of 50 Hz is 43 cm or 0.43 m, which corresponds to answer choice D.

Question 15

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 is given by:
f = (1/2L) * sqrt(Tension/linear density)

Where L is the length of the string (in this case 200 cm), Tension is the tension applied to the string (600 N), and linear density is the density of the string (0.015 g/cm).

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

Therefore, the answer is option C, with a fundamental frequency of 158 Hz.

Question 16

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

When a string is divided into three equal segments, the fundamental frequency is three times the frequency of the first harmonic. Therefore, the fundamental frequency of the string is 3 x 160 Hz = 480 Hz. Thus, the correct answer is (C).

Question 17

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 18

The path difference between two waves is 5m. If the wavelength of the waves emitted by the two sources is 4m, 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 19

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

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

Question 20

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...

Quiz 18: Superposition and Standing Waves

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.

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

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

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

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?

Two harmonic waves are described by What is the magnitude of the displacement (in cm) of this wave at x = 3 cm and t = 5 sec?

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

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 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 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?

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 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 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 are described by What is the amplitude of the resultant wave?

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

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?