Question 1

A stretched string is observed to have four equal segments in a standing wave driven at a frequency of 480 Hz. What driving frequency will set up a standing wave with five equal
Segments?
A) 120 Hz
B) 240 Hz
C) 600 Hz
D) 360 Hz

Accepted Answer

The frequency required to set up a standing wave with a certain number of segments (or antinodes) is directly proportional to the number of segments. If 4 segments correspond to 480 Hz, then 5 segments, which is 1.25 times more segments, will require 1.25 times the frequency, which is 480 Hz * 1.25 = 600 Hz.

Question 2

If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz?
A) 1450 Hz
B) 4560 Hz
C) 2.54 Hz
D) 3.98 Hz
E) 1.27 Hz

Accepted Answer

The frequency in hertz (Hz) is the number of cycles (in this case, heartbeats) per second. To convert beats per minute to hertz, divide the number of beats by 60 (since there are 60 seconds in a minute). Therefore, 76 beats per minute is 76/60 = 1.27 Hz.

Question 3

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of
These two systems?
A) The period of the pendulum would increase but the period of the spring would stay the same.
B) The period of the pendulum would decrease but the period of the spring would stay the same.
C) Both periods would remain the same.
D) Both periods would increase.
E) Both periods would decrease.

Accepted Answer

The period of a simple pendulum depends on the acceleration due to gravity and the length of the pendulum, but not on the horizontal or vertical velocity of the system. Similarly, the period of a mass oscillating on an ideal spring depends on the mass and the spring constant, but not on the system's uniform motion. Therefore, if the elevator moves downward at a uniform speed, neither the gravitational acceleration experienced by the pendulum nor the properties of the spring-mass system change, so both periods remain the same.

Question 4

A guitar string is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo each minute?
A) 512
B) 8.53
C) 1610
D) 26.8
E) 30,700

Accepted Answer

The guitar string vibrates at 512 Hz, which means it completes 512 oscillations per second. To find the number of oscillations per minute, multiply by 60 seconds: 512 oscillations/second * 60 seconds/minute = 30,720 oscillations/minute.

Question 5

A 1.53-kg piece of iron is hung by a vertical ideal spring. When perturbed slightly, the system is moves up and down in simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude
Of 7.50 cm. If we choose the total potential energy (elastic and gravitational) to be zero at the
Equilibrium position of the hanging iron, what is the total mechanical energy of the system?
A) 0.955 J
B) 0.633 J
C) 0.844 J
D) 0.646 J
E) 0.000 J

Accepted Answer

The answer of A 1.53-kg piece of iron is hung...

Question 6

What is the length of a simple pendulum with a period of 2.0 s?
A) 0.99 m
B) 0.87 m
C) 1.6 m
D) 20 m
E) 1.2 m

Accepted Answer

The period $T$ of a simple pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity ($9.8 \, \text{m/s}^2$). Rearranging for $L$, we get $L = \frac{gT^2}{4\pi^2}$. Substituting $T = 2.0 \, \text{s}$ and $g = 9.8 \, \text{m/s}^2$, we find $L \approx 0.99 \, \text{m}$.

Question 7

A leaky faucet drips 40 times in 30.0 s. What is the frequency of the dripping?
A) 0.63 Hz
B) 1.6 Hz
C) 0.75 Hz
D) 1.3 Hz

Accepted Answer

The answer of A leaky faucet drips 40 times in...

Question 8

A string fixed at both ends is vibrating in one of its harmonics. If we now increase only the frequency at which the string is vibrating, which of the following characteristics do we also
Increase? (There could be more than one correct choice.)
A) the amplitude of the traveling waves on the string
B) the wavelength of the traveling waves on the string
C) the period of the traveling waves on the string
D) the speed of the traveling waves on the string
E) none of the above

Accepted Answer

Increasing the frequency of vibration in a string fixed at both ends (assuming the tension and linear density of the string remain constant) does not inherently increase the amplitude, wavelength, period, or speed of the traveling waves. The speed of wave propagation in a string is determined by the tension and mass per unit length of the string, not by the frequency. The wavelength is inversely related to the frequency for a given wave speed, but increasing the frequency does not increase the wavelength; it decreases it. The amplitude of the wave is independent of the frequency and depends on the energy put into the system. The period is the inverse of frequency, so increasing the frequency decreases the period, not increases it.

Question 9

The speed of sound in steel is 5000 m/s. What is the wavelength of a sound wave of frequency 660 Hz in steel?
A) 0.829 m
B) 2.41 m
C) 0.132 m
D) 1.21 m
E) 7.58 m

Accepted Answer

The answer of The speed of sound in steel is...

Question 10

A 0.150-kg cart that is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m undergoes simple harmonic oscillations with an amplitude of 7.50 cm. What is the total
Mechanical energy of the system?
A) 0.0201 J
B) 0.134 J
C) 0.269 J
D) 0.0101 J
E) 0 J

Accepted Answer

The answer of A 0.150-kg cart that is attached to...

Question 11

Crests of an ocean wave pass a pier every 10.0 s. If the waves are moving at 5.6 m/s, what is the wavelength of the ocean waves?
A) 64 m
B) 28 m
C) 48 m
D) 56 m

Accepted Answer

The wavelength can be calculated using the formula: wavelength = speed x period. The period is 10.0 s, and the speed is 5.6 m/s. Therefore, the wavelength is 5.6 m/s * 10.0 s = 56 m.

Question 12

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s², what is true about the periods
Of these two systems?
A) The period of the pendulum would decrease but the period of the spring would stay the same.
B) Both periods would remain the same.
C) Both periods would decrease.
D) Both periods would increase.
E) The period of the pendulum would increase but the period of the spring would stay the same.

Accepted Answer

The period of a simple pendulum depends on the acceleration due to gravity (g). If the elevator accelerates downward, the effective acceleration due to gravity decreases, which increases the period of the pendulum. The period of a mass oscillating on an ideal spring depends on the mass and the spring constant, not on gravity, so it remains unchanged.

Question 13

How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 N/m so that it will oscillate at 1.00 Hz?
A) 1.00 kg
B) 1.56 kg
C) 2.00 kg
D) 6.29 kg
E) 39.5 kg

Accepted Answer

The frequency of oscillation $f$ for a mass $m$ attached to a spring with spring constant $k$ is given by $f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$. Rearranging to solve for $m$, we get $m = \frac{k}{(2\pi f)^2}$. Substituting $k = 39.5 \, \text{N/m}$ and $f = 1.00 \, \text{Hz}$, we find $m = 1.00 \, \text{kg}$.

Question 14

If a string fixed at both ends resonates in its fundamental mode with a frequency of 150 Hz, at which of the following frequencies will it not resonate? (There could be more than one correct
Choice.)
A) 450 Hz
B) 75 Hz
C) 500 Hz
D) 300 Hz
E) 600 Hz

Accepted Answer

A string fixed at both ends resonates at its fundamental frequency and its harmonics, which are integer multiples of the fundamental frequency. The fundamental frequency is 150 Hz, so the harmonics are 150 Hz, 300 Hz, 450 Hz, 600 Hz, etc. 75 Hz is not a multiple of 150 Hz, and 500 Hz is also not a multiple of 150 Hz, so the string will not resonate at these frequencies.

Question 15

A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cables for the swing is 4.9 m, how long does it take for each complete
Back-and-forth swing? Assume that the child and swing set are very small compared to the length
Of the cables.
A) 5.3 s
B) 5.7 s
C) 4.8 s
D) 4.4 s

Accepted Answer

The period of a pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Plugging in the given length $L = 4.9 \, \text{m}$, we get $T = 2\pi\sqrt{\frac{4.9}{9.8}} = 2\pi\sqrt{0.5} = \pi$. Since $\pi \approx 3.14$, $T \approx 3.14 \times 1.4 = 4.4 \, \text{s}$. Note that the mass of the child and swing set does not affect the period of the swing, as the formula for the period of a pendulum does not include mass.

Question 16

A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20 N/m. If the amplitude of this motion is 0.30 m, what is the kinetic energy of the ball
When it is 0.30 m from its equilibrium position?
A) 0.00 J
B) 1.4 J
C) 0.45 J
D) 0.90 J
E) 0.22 J

Accepted Answer

At 0.30 m from its equilibrium position, the ball is at its maximum displacement (amplitude), meaning all its energy is potential and its kinetic energy is 0.00 J because it momentarily stops before changing direction.

Question 17

An object is undergoing simple harmonic motion of amplitude 2.3 m. If the maximum velocity of the object is 10 m/s, what is the object's angular frequency?
A) 4.8 rad/s
B) 4.0 rad/s
C) 3.5 rad/s
D) 4.3 rad/s

Accepted Answer

The maximum velocity $v_{max}$ in simple harmonic motion is given by the formula $v_{max} = \omega A$, where $\omega$ is the angular frequency and $A$ is the amplitude. Rearranging for $\omega$, we get $\omega = \frac{v_{max}}{A}$. Substituting the given values, $\omega = \frac{10 \, \text{m/s}}{2.3 \, \text{m}} = 4.3478 \, \text{rad/s}$, which rounds to $4.3 \, \text{rad/s}$.

Question 18

Transverse waves travel at 43.2 m/s in a string that is subjected to a tension of 60.5 N. If the string is 15.9 m long, what is its mass?
A) 0.515 kg
B) 0.597 kg
C) 0.216 kg
D) 0.366 kg

Accepted Answer

The mass of the string can be calculated using the wave speed formula for a string, $v = \sqrt{\frac{T}{\mu}}$, where $v$ is the wave speed, $T$ is the tension in the string, and $\mu$ is the mass per unit length of the string. Rearranging this formula to solve for $\mu$ gives $\mu = \frac{T}{v^2}$. The total mass of the string ($m$) can then be found by multiplying $\mu$ by the length of the string ($L$), so $m = \mu L = \frac{T}{v^2} \times L$. Substituting the given values, $T = 60.5 \, \text{N}$, $v = 43.2 \, \text{m/s}$, and $L = 15.9 \, \text{m}$, we find $m = \frac{60.5}{43.2^2} \times 15.9 \approx 0.515 \, \text{kg}$.

Question 19

A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of
1)5 m/s at the equilibrium position. At what distance from the equilibrium position are the kinetic
Energy and potential energy of the system the same?
A) 0.029 m
B) 0.12 m
C) 0.17 m
D) 0.017 m

Accepted Answer

The answer of A 0.50-kg object is attached to an...

Question 20

The position of an object that is oscillating on a spring is given by the equation x = (17.4 cm) cos[(5.46 s-1)t]. What is the angular frequency for this motion?
A) 0.869 rad/s
B) 2.34 rad/s
C) 17.4 rad/s
D) 0.183 rad/s
E) 5.46 rad/s

Accepted Answer

The angular frequency for oscillatory motion is given directly by the coefficient of $t$ in the cosine function of the position equation, which in this case is $5.46 \, \text{s}^{-1}$, corresponding to $5.46 \, \text{rad/s}$.

Quiz 2: Describing Motion: Kinematics in One Dimension

A stretched string is observed to have four equal segments in a standing wave driven at a frequency of 480 Hz. What driving frequency will set up a standing wave with five equal Segments?

If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz?

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of These two systems?

A guitar string is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo each minute?

What is the length of a simple pendulum with a period of 2.0 s?

A leaky faucet drips 40 times in 30.0 s. What is the frequency of the dripping?

A string fixed at both ends is vibrating in one of its harmonics. If we now increase only the frequency at which the string is vibrating, which of the following characteristics do we also Increase? (There could be more than one correct choice.)

The speed of sound in steel is 5000 m/s. What is the wavelength of a sound wave of frequency 660 Hz in steel?

A 0.150-kg cart that is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m undergoes simple harmonic oscillations with an amplitude of 7.50 cm. What is the total Mechanical energy of the system?

Crests of an ocean wave pass a pier every 10.0 s. If the waves are moving at 5.6 m/s, what is the wavelength of the ocean waves?

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s², what is true about the periods Of these two systems?

How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 N/m so that it will oscillate at 1.00 Hz?

If a string fixed at both ends resonates in its fundamental mode with a frequency of 150 Hz, at which of the following frequencies will it not resonate? (There could be more than one correct Choice.)

A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20 N/m. If the amplitude of this motion is 0.30 m, what is the kinetic energy of the ball When it is 0.30 m from its equilibrium position?

An object is undergoing simple harmonic motion of amplitude 2.3 m. If the maximum velocity of the object is 10 m/s, what is the object's angular frequency?

Transverse waves travel at 43.2 m/s in a string that is subjected to a tension of 60.5 N. If the string is 15.9 m long, what is its mass?

The position of an object that is oscillating on a spring is given by the equation x = (17.4 cm) cos[(5.46 s-1) t]. What is the angular frequency for this motion?