Question 1

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz. The maximum speed of any point on the string is:
A) 2.0 m/s
B) 4.0 m/s
C) 6.3 m/s
D) 13 m/s
E) unknown (not enough information is given)

Accepted Answer

The answer of A string carries a sinusoidal wave with...

Question 2

A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. The maximum acceleration of any point on the string is: A) 0 m/s² B) 200 m/s² C) 390 m/s² D) 790 m/s² E) 1600 m/s²

Accepted Answer

The answer of A transverse traveling sinusoidal wave on a...

Question 3

For a given medium, the frequency of a wave is:
A) independent of wavelength
B) proportional to wavelength
C) inversely proportional to wavelength
D) proportional to the amplitude
E) inversely proportional to the amplitude

Accepted Answer

The frequency of a wave is inversely proportional to its wavelength. This is described by the relationship f = c/λ, where f is frequency, λ (lambda) is wavelength, and c is the speed of light (or the speed that the wave travels through the given medium). As wavelength increases, frequency decreases, and vice versa.

Question 4

A long string is constructed by joining the ends of two shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:
A) the frequency decreases by a factor of 4
B) the frequency decreases by a factor of 2
C) the wavelength decreases by a factor of 4
D) the wavelength decreases by a factor of 2
E) the wavelength increases by a factor of 2

Accepted Answer

When a wave passes from one medium to another, the frequency remains constant. Therefore, options A and B can be eliminated. However, the speed of the wave changes as it moves from one medium to another. The speed of a wave is given by the product of its frequency and wavelength. Therefore, if the frequency remains constant and the speed of the wave changes, the wavelength must also change.

Using the formula v = fλ, we can see that for a given tension, the speed of the wave is the same for both strings. Since string I has 4 times the linear mass density of string II, its wave speed is also 4 times slower than that of string II. Therefore, as the wave passes from string I to string II, its wavelength must decrease by a factor of 4/1 = 4. Therefore, the correct answer is D.

Question 5

A wave traveling to the right on a stretched string is shown below. The direction of the instantaneous velocity of the point P on the string is: 
A)$\uparrow$
B) $\downarrow$
C) $\rightarrow$
D) 
E) no direction since v = 0

Accepted Answer

The answer of A wave traveling to the right on...

Question 6

Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The angular frequency is given by:
A) 1/T
B) 2$\pi$/T
C) vT
D) f/T
E) T/f

Accepted Answer

The angular frequency of a sinusoidal wave is given by $2\pi f$, where $f$ is the frequency of the wave. Since the frequency $f$ is the reciprocal of the period $T$ (i.e., $f = 1/T$), the angular frequency can also be expressed as $2\pi/T$, which matches the form given in option B.

Question 7

Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz. The speed of these waves is:
A) 0.00023 m/s
B) 2.1 m/s
C) 21 m/s
D) 4300 m/s
E) none of these

Accepted Answer

The speed of water waves can be found using the formula: 
speed = wavelength × frequency 
Substituting the given values, we get: 
speed = 300 m × 0.07 Hz 
speed = 21 m/s 
Therefore, the correct answer is choice C.

Question 8

The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is: 
A) $\uparrow$
B) $\downarrow$
C) $\rightarrow$
D) 
E) no direction since v = 0

Accepted Answer

The answer of The transverse wave shown is traveling from...

Question 9

A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. The maximum velocity of any point on the string is:
A) 0.20 m/s
B) 1.3 m/s
C) 4.0 m/s
D) 15 m/s
E) 25 m/s

Accepted Answer

The maximum velocity ($v_{max}$) of a point on a wave is given by the formula $v_{max} = 2\pi fA$, where $f$ is the frequency and $A$ is the amplitude. Given that the frequency $f = 100$ Hz and the amplitude $A = 2.0$ mm $= 0.002$ m, substituting these values gives $v_{max} = 2\pi \times 100 \times 0.002 = 1.256$, which rounds to $1.3$ m/s.

Question 10

Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The correct relationship is:
A) f = 1/T
B) f = v + T
C) f = vT
D) f = v/T
E) f = T/v

Accepted Answer

The equation for the frequency of a wave is f = 1/T, where T is the period of the wave. This means that the frequency is inversely proportional to the period, so as the period increases, the frequency decreases and vice versa. None of the other options are correct relationships between frequency, speed, and period.

Question 11

The mathematical forms for the three sinusoidal traveling waves are given by  where x is in meters and t is in seconds. Of these waves:
A) wave 1 has the greatest wave speed and the greatest maximum transverse string speed
B) wave 2 has the greatest wave speed and wave 1 has the greatest maximum transverse string speed
C) wave 3 has the greatest wave speed and the greatest maximum transverse string speed
D) wave 2 has the greatest wave speed and wave 3 has the greatest maximum transverse string speed
E) wave 3 has the greatest wave speed and wave 2 has the greatest maximum transverse string speed

Accepted Answer

The answer of The mathematical forms for the three sinusoidal...

Question 12

A transverse wave travels on a string of length 1.3 m and diameter 1.1 mm, whose mass is 10 g and which is under a tension of 16 N. What is the linear mass density of the string? A) 7.7 x 10^-3 kg/m B) 0.13 kg/m C) 7.7 kg/m D) 46 kg/m E) 130 kg/m

Accepted Answer

The linear mass density ($\mu$) is given by:
$$\mu = \frac{m}{L}$$
where $m$ is the mass of the string and $L$ is its length. Substituting $m=10	ext{ g}=10	imes 10^{-3}	ext{ kg}$ and $L=1.3	ext{ m}$, we get:
$$\mu = \frac{10	imes 10^{-3}	ext{ kg}}{1.3	ext{ m}} = 7.7	imes 10^{-3}	ext{ kg/m}$$
However, the diameter of the string is given instead of its radius. Therefore, we need to convert the diameter ($d$) to radius ($r$) using:
$$r = \frac{d}{2}$$
Substituting $d=1.1	ext{ mm}$, we get:
$$r = \frac{1.1	imes 10^{-3}	ext{ m}}{2} = 0.55	imes 10^{-3}	ext{ m}$$
The tension ($T$) in the string is related to the wave speed ($v$) and the linear mass density ($\mu$) by:
$$v = \sqrt{\frac{T}{\mu}}$$
Squaring both sides and rearranging, we get:
$$\mu = \frac{T}{v^2}$$
Substituting $T=16	ext{ N}$ and rearranging, we get:
$$\mu = \frac{16	ext{ N}}{v^2}$$
The speed of the wave is related to the tension ($T$) and the linear mass density ($\mu$) by:
$$v = \sqrt{\frac{T}{\mu}}$$
Rearranging, we get:
$$\mu = \frac{T}{v^2}$$
Substituting $T=16	ext{ N}$ and $v=\sqrt{\frac{T}{\mu}}$, we get:
$$\mu = \frac{16	ext{ N}}{\left(\sqrt{\frac{16	ext{ N}}{7.7	imes 10^{-3}	ext{ kg/m}}}ight)^2} \approx 7.7	ext{ x }10^{-3}	ext{ kg/m}$$
Therefore, the answer is A.

Question 13

Suppose the maximum speed of a string carrying a sinusoidal wave is v_s. When the displacement of a point on the string is half its maximum, the speed of the point is: A) v_s/2 B) 2v_s C) v_s/4 D) 3v_s/4 E)

Accepted Answer

The answer of Suppose the maximum speed of a string...

Question 14

Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:
A) the magnitude of its acceleration is a maximum
B) the magnitude of its displacement is a maximum
C) the magnitude of its displacement is a minimum
D) the magnitude of its displacement is half the amplitude
E) the magnitude of its displacement is one fourth the amplitude

Accepted Answer

The velocity of a point on a string carrying a sinusoidal wave is zero at the nodes (points of zero displacement) and maximum at the antinodes (points of maximum displacement). Therefore, a point on the string will be moving with its maximum speed when the magnitude of its displacement is a minimum (at a node). At this point, the string is changing direction instantaneously, and so its velocity is changing rapidly. The magnitude of acceleration is greatest at the points of maximum displacement (the antinodes).

Question 15

A source of frequency f sends waves of wavelength $\lambda$ traveling with speed v in some medium. If the frequency is changed from f to 2f, then the new wavelength and new speed are (respectively):
A) 2$\lambda$, v
B) $\lambda$/2, v
C) $\lambda$, 2v
D) $\lambda$, v/2
E)$\lambda$/2, 2v

Accepted Answer

The speed of wave propagation in a medium is constant for a given frequency and does not depend on the frequency. Therefore, if the frequency is doubled, the wavelength is halved to maintain the same wave speed.

Question 16

A sinusoidal transverse wave is traveling on a string. Any point on the string:
A) moves in the same direction as the wave
B) moves in simple harmonic motion with a different frequency than that of the wave
C) moves in simple harmonic motion with the same angular frequency as the wave
D) moves in uniform circular motion with a different angular speed than the wave
E) moves in uniform circular motion with the same angular speed as the wave

Accepted Answer

Any point on a string that is experiencing a sinusoidal transverse wave will move in simple harmonic motion with the same angular frequency as the wave. This means that the point will move back and forth in a straight line, perpendicular to the direction of the wave, with a frequency equal to the wave's frequency.

Question 17

In the figure, a wave is traveling from left to right. If the point marked "D" represents the origin at time t = 0, and the displacement of the wave is given by y(x,t) = y_msin(kx - $ \omega $t - $\phi$ ), what is the phase constant $\phi$ A) 0 B) π/6 C) π/4 D) π/2 E) 3π/2

Accepted Answer

The answer of In the figure, a wave is traveling...

Question 18

Here are equations for three waves traveling on separate strings. Rank them according to the maximum transverse speed, least to greatest. 
A) 1, 2, 3
B) 1, 3, 2
C) 2, 1, 3
D) 2, 3, 1
E) 3, 1, 2

Accepted Answer

The answer of Here are equations for three waves traveling...

Question 19

Sinusoidal water waves are generated in a large ripple tank. The waves travel at 20 cm/s and their adjacent crests are 5.0 cm apart. The time required for each new whole cycle to be generated is:
A) 100 s
B) 4.0 s
C) 2.0 s
D) 0.5 s
E) 0.25 s

Accepted Answer

The time required for each new whole cycle to be generated, also known as the period (T), can be found using the formula T = wavelength / speed. Given the wavelength is 5.0 cm (or 0.05 m) and the speed is 20 cm/s (or 0.20 m/s), T = 0.05 m / 0.20 m/s = 0.25 s.

Question 20

Sinusoidal waves travel on five identical strings. Four of the strings have the same tension, but the fifth has a different tension. Use the mathematical forms of the waves, gives below, to identify the string with the different tension. In the expressions given below x and y are in centimeters and t is in seconds.
A) y(x,t) = (2 cm) sin (2x - 4t)
B) y(x,t) = (2 cm) sin (4x - 10t)
C) y(x,t) = (2 cm) sin (6x - 12t)
D) y(x,t) = (2 cm) sin (8x - 16t)
E) y(x,t) = (2 cm) sin (10x - 20t)

Accepted Answer

The wave speed $v$ in a string is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the mass per unit length of the string. The phase velocity of a wave is given by $v = \frac{\omega}{k}$, where $\omega$ is the angular frequency and $k$ is the wave number. In the given equations, the term in the sine function can be written as $kx - \omega t$, where $k$ is the coefficient of $x$ and $\omega$ is the coefficient of $t$. For strings A, C, D, and E, the ratio $\frac{\omega}{k}$ is constant (2 for A, 2 for C, 2 for D, and 2 for E), indicating the same wave speed and thus the same tension. However, for string B, this ratio is $\frac{10}{4} = 2.5$, which is different, indicating a different tension in the string.

Quiz 16: Waves I

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz. The maximum speed of any point on the string is:

A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. The maximum acceleration of any point on the string is:

For a given medium, the frequency of a wave is:

A long string is constructed by joining the ends of two shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The angular frequency is given by:

Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz. The speed of these waves is:

A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. The maximum velocity of any point on the string is:

Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The correct relationship is:

The mathematical forms for the three sinusoidal traveling waves are given by where x is in meters and t is in seconds. Of these waves:

A transverse wave travels on a string of length 1.3 m and diameter 1.1 mm, whose mass is 10 g and which is under a tension of 16 N. What is the linear mass density of the string?

Suppose the maximum speed of a string carrying a sinusoidal wave is v_s. When the displacement of a point on the string is half its maximum, the speed of the point is:

Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:

A source of frequency f sends waves of wavelength $\lambda$ traveling with speed v in some medium. If the frequency is changed from f to 2f, then the new wavelength and new speed are (respectively) :

A sinusoidal transverse wave is traveling on a string. Any point on the string:

Here are equations for three waves traveling on separate strings. Rank them according to the maximum transverse speed, least to greatest.

Sinusoidal water waves are generated in a large ripple tank. The waves travel at 20 cm/s and their adjacent crests are 5.0 cm apart. The time required for each new whole cycle to be generated is: