Question 1

A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 115 N.If the distance between the points is changed by 1.0%,then what is the percentage change of the frequency?
A) 0.50%
B) 0.75%
C) 1.00%
D) 1.25%
E) 1.50%

Accepted Answer

The frequency of a stretched string is given by:
f = (1/2L)√(T/μ)
where L is the length of the string, T is the tension and μ is the mass per unit length.

Now, if the tension is kept constant and the length is changed by ΔL, then the new frequency f' is given by:

f' = (1/2(L+ΔL))√(T/μ)

So, the percentage change in frequency is given by:

Δf/f = (f' - f)/f = [(1/2(L+ΔL))√(T/μ) - (1/2L)√(T/μ)]/[(1/2L)√(T/μ)]

= (ΔL/L)/(2√(T/μ)) = 0.01/(2√(115/0.002)) = 0.375%

Therefore, the answer is C, 1.00%.

Question 2

The wavelength of a periodic wave is 0.750 m.If the frequency is 425 Hz,then what is the velocity of the wave?
A) 210 m/s
B) 276 m/s
C) 319 m/s
D) 410 m/s
E) 472 m/s

Accepted Answer

The formula for the velocity of a wave is V = fλ, where V is the velocity, f is the frequency, and λ is the wavelength. 
Plugging in the given values, V = (425 Hz)(0.750 m) = 318.75 m/s which is closest to option C, 319 m/s.

Question 3

A wave travels at 175 m/s along the x-axis.If the period of the periodic vibrations of the wave is 3.00 milliseconds,then what is the wavelength of the wave?
A) 25.5 cm
B) 35.6 cm
C) 42.9 cm
D) 49.5 cm
E) 52.5 cm

Accepted Answer

The answer of A wave travels at 175 m/s along...

Question 4

Visible light consists of electromagnetic waves with wavelengths (in air)in the range 400 - 700 nm.What are the frequencies of visible light? A) 1.33 $\times$ 10¹⁴ Hz to 2.33 $\times$ 10¹⁴ Hz B) 1.33 $\times$ 10¹² Hz to 2.33 $\times$ 10¹² Hz C) 4.28 $\times$ 10¹² Hz to 7.50 $\times$ 10¹² Hz D) 4.28 $\times$ 10¹⁴ Hz to 7.50 $\times$ 10¹⁴ Hz

Accepted Answer

The frequency of light is calculated using the formula: frequency = speed of light / wavelength. For visible light, with wavelengths 400 nm to 700 nm, the frequencies are approximately 7.50 * 10^14 Hz to 4.28 * 10^14 Hz.

Question 5

A transverse wave travels at 190 m/s along the x-axis.If the period of the periodic vibrations of the wave is 2.6 milliseconds,then what is the wavelength of the wave?
A) 25.5 cm
B) 35.4 cm
C) 49.4 cm
D) 50.3 cm
E) 54.4 cm

Accepted Answer

We can use the formula:
wavelength = velocity/frequency
where velocity = 190 m/s (given)
frequency = 1/period = 1/(2.6 x 10^-3 s) = 384.6 Hz
Plugging in the values, we get:
wavelength = 190/384.6 = 0.494 m = 49.4 cm. Therefore, the wavelength is 49.4 cm.

Question 6

The wavelength of a periodic wave is 0.750 m.If the frequency is 425 Hz,then what is the angular frequency,$\omega$,of the wave? A) 5.44 $\times$ 10³ rad/s B) 5.03 $\times$ 10³ rad/s C) 4.21 $\times$ 10³ rad/s D) 3.76 $\times$ 10³ rad/s E) 2.67 $\times$ 10³ rad/s

Accepted Answer

The answer of The wavelength of a periodic wave is...

Question 7

The frequency of a periodic wave is 325 Hz.If the wavelength is 50.0 cm,then what is the velocity of the wave?
A) 163 m/s
B) 203 m/s
C) 237 m/s
D) 285 m/s
E) 316 m/s

Accepted Answer

The velocity of a wave is calculated using the formula velocity = frequency × wavelength. Given the frequency is 325 Hz and the wavelength is 50.0 cm (which needs to be converted to meters, thus 0.50 m), the velocity = 325 Hz × 0.50 m = 162.5 m/s, which rounds to 163 m/s.

Question 8

A transverse wave travels at 230.0 m/s along the y-axis.If the frequency of the periodic vibrations of the wave is 390.0 Hz,then what is the wavelength of the wave?
A) 58.97 cm
B) 47.23 cm
C) 40.89 cm
D) 36.76 cm
E) 68.97 cm

Accepted Answer

The answer of A transverse wave travels at 230.0 m/s...

Question 9

The wavelength of a periodic wave is 0.800 m.If the frequency is 400 Hz,then what is the magnitude of the k vector of the wave? A) 8.56 m^-1 B) 7.85 m^-1 C) 7.02 m^-1 D) 6.35 m^-1 E) 5.98 m^-1

Accepted Answer

The magnitude of the wave vector k is given by the formula k = 2π/λ. Substituting λ = 0.800 m, we get k = 2π/0.800 = 7.85 m^-1.

Question 10

A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 120 N.If the fundamental frequency is 660 Hz,then what is the distance between the two points?
A) 17.5 cm
B) 18.6 cm
C) 20.3 cm
D) 26.7 cm
E) 30.0 cm

Accepted Answer

The speed of a wave on a string is given by the equation:
v = sqrt(T/u)
where T is the tension in the string and u is the linear density (mass/length).
Substituting the given values, we get:
v = sqrt(120/0.00200) = 154.92 m/s
The wavelength of the fundamental mode of vibration is twice the length of the string, so we have:
lambda = 2L
f = v/lambda
where f is the frequency of the wave.
Substituting the given values and solving for L, we get:
L = v/2f = 154.92/(2*660) = 0.117 m
Converting to centimeters, we get:
L = 11.7 cm
Since L is only half the distance between the two points, the actual distance between the two points is:
2L = 2*11.7 = 23.4 cm
which is closest to choice B (18.6 cm).

Question 11

Of these properties of waves,which one is independent of the others?
A) amplitude
B) speed
C) frequency
D) wavelength

Accepted Answer

Amplitude is independent of the other properties, as it relates to the energy of the wave and does not affect or is affected by speed, frequency, or wavelength.

Question 12

The frequency of a periodic wave is 340 Hz.The period of the vibration motion of the wave is
A) 2.56 milliseconds.
B) 2.94 milliseconds.
C) 3.55 milliseconds.
D) 3.94 milliseconds.
E) 4.25 milliseconds.

Accepted Answer

Recall that frequency and period are reciprocals of each other:

frequency = 1/period

Therefore, we can solve for the period by taking the reciprocal of the frequency:

period = 1/frequency = 1/340 Hz = 2.94 milliseconds

Therefore, the answer is choice B.

Question 13

A transverse wave travels at 250 m/s along the z-axis.If the frequency of the periodic vibrations of the wave is 440 Hz,then what is the wavelength of the wave?
A) 21.9 cm
B) 26.7 cm
C) 35.7 cm
D) 56.8 cm
E) 73.7 cm

Accepted Answer

The answer of A transverse wave travels at 250 m/s...

Question 14

Two strings on a violin are stretched between two points 20 cm apart.The tensions of the strings are the same.If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0,then what is the ratio of the mass per lengths in the strings?
A) 0.80
B) 0.90
C) 0.85
D) 0.94
E) 0.78

Accepted Answer

The frequency of a string is given by:f = (1/2L) * sqrt(T/m)where L is the length of the string, T is the tension, and m is the mass per length.If the tensions are the same, then the ratio of the frequencies is:f1/f2 = sqrt(m2/m1)where m1 and m2 are the mass per lengths of the strings.If the ratio of the frequencies is 1.5 to 1.0, then:1.5 = sqrt(m2/m1)m2/m1 = 2.25m2 = 2.25 * m1Therefore, the ratio of the mass per lengths in the strings is 2.25 to 1.0, which is closest to choice A) 0.80.

Question 15

Two strings on a violin are stretched between two points 20.0 cm apart.The mass per length of the strings are the same.If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0,then what is the ratio of the tensions in the strings?
A) 1.75
B) 1.88
C) 1.00
D) 1.25
E) 1.50

Accepted Answer

The answer of Two strings on a violin are stretched...

Question 16

The wavelength of a periodic wave is 0.750 m.If the frequency is 365 Hz,then what is the angular frequency,$\omega$,of the wave? A) 3.87 $\times$ 10³ rad/s B) 3.10 $\times$ 10³ rad/s C) 2.98 $\times$ 10³ rad/s D) 2.29 $\times$ 10³ rad/s E) 1.75 $\times$ 10³ rad/s

Accepted Answer

The answer of The wavelength of a periodic wave is...

Question 17

The speed of waves in stretched string depends on which of the following?
A) the tension in the string
B) the amplitude of the waves
C) the wavelength of the waves
D) the frequency of the waves

Accepted Answer

The speed of waves in a stretched string is directly proportional to the tension in the string. This means that as tension increases, so does wave speed. The amplitude, wavelength, and frequency of the waves do not affect the speed of waves in a stretched string.

Question 18

The period of a periodic wave is 2.80 milliseconds.The frequency of the vibration motion of the wave is
A) 450 Hz.
B) 437 Hz.
C) 402 Hz.
D) 357 Hz.
E) 306 Hz.

Accepted Answer

The answer of The period of a periodic wave is...

Question 19

A string on a violin is stretched between two points 20.00 cm apart with a tension of 120.0 N.The mass/length of the string is 0.002000 kg/m.The frequency of the 2^nd overtone is A) 1,502 Hz. B) 1,837 Hz. C) 2,237 Hz. D) 2,568 Hz. E) 3,250 Hz.

Accepted Answer

The answer of A string on a violin is stretched...

Question 20

A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 120 N.If the fundamental frequency is 440 Hz,then what is the distance between the two points?
A) 17.5 cm
B) 20.3 cm
C) 27.8 cm
D) 30.0 cm
E) 35.0 cm

Accepted Answer

The speed of a wave on a string is given by:
v = √(T/μ)
where T is the tension and μ is the mass per unit length.

The frequency of the wave is given by:
f = (1/2L) √(T/μ)
where L is the length of the string.

Solving for L, we get:
L = (1/2) √(T/μ) / f

Plugging in the given values, we get:
L = (1/2) √(120 N / 0.00200 kg/m) / 440 Hz
L = 0.2778 m = 27.8 cm

Therefore, the answer is C) 27.8 cm.

Quiz 11: Waves

A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 115 N.If the distance between the points is changed by 1.0%,then what is the percentage change of the frequency?

The wavelength of a periodic wave is 0.750 m.If the frequency is 425 Hz,then what is the velocity of the wave?

A wave travels at 175 m/s along the x-axis.If the period of the periodic vibrations of the wave is 3.00 milliseconds,then what is the wavelength of the wave?

Visible light consists of electromagnetic waves with wavelengths (in air) in the range 400 - 700 nm.What are the frequencies of visible light?

A transverse wave travels at 190 m/s along the x-axis.If the period of the periodic vibrations of the wave is 2.6 milliseconds,then what is the wavelength of the wave?

The wavelength of a periodic wave is 0.750 m.If the frequency is 425 Hz,then what is the angular frequency, $\omega$ ,of the wave?

The frequency of a periodic wave is 325 Hz.If the wavelength is 50.0 cm,then what is the velocity of the wave?

A transverse wave travels at 230.0 m/s along the y-axis.If the frequency of the periodic vibrations of the wave is 390.0 Hz,then what is the wavelength of the wave?

The wavelength of a periodic wave is 0.800 m.If the frequency is 400 Hz,then what is the magnitude of the k vector of the wave?

A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 120 N.If the fundamental frequency is 660 Hz,then what is the distance between the two points?

Of these properties of waves,which one is independent of the others?

The frequency of a periodic wave is 340 Hz.The period of the vibration motion of the wave is

A transverse wave travels at 250 m/s along the z-axis.If the frequency of the periodic vibrations of the wave is 440 Hz,then what is the wavelength of the wave?

Two strings on a violin are stretched between two points 20 cm apart.The tensions of the strings are the same.If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0,then what is the ratio of the mass per lengths in the strings?

Two strings on a violin are stretched between two points 20.0 cm apart.The mass per length of the strings are the same.If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0,then what is the ratio of the tensions in the strings?

The wavelength of a periodic wave is 0.750 m.If the frequency is 365 Hz,then what is the angular frequency, $\omega$ ,of the wave?

The speed of waves in stretched string depends on which of the following?

The period of a periodic wave is 2.80 milliseconds.The frequency of the vibration motion of the wave is

A string on a violin is stretched between two points 20.00 cm apart with a tension of 120.0 N.The mass/length of the string is 0.002000 kg/m.The frequency of the 2^nd overtone is

A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 120 N.If the fundamental frequency is 440 Hz,then what is the distance between the two points?