Question 1

Two speakers next to each other oscillate in phase,one at 404 Hz and the other at 400 Hz.If you stand in front of them,you will hear a sound of frequency 402 Hz that fluctuates between loud and soft with a frequency of 4 Hz.

Accepted Answer

This phenomenon is known as beats, which occurs when two sounds of slightly different frequencies are played together. The frequency of the beat is equal to the difference between the two frequencies, which in this case is 4 Hz. This creates the perception of a fluctuating loudness of the sound, but the average frequency heard is the average of the two original frequencies, which is 402 Hz.

Question 2

A string 2.0 m long and fixed at both ends is vibrating in its fourth harmonic in a room at 20C.The wavelength of the sound it produces is 1.0 m.

Accepted Answer

The wavelength of a sound wave is given by the formula λ = 2L/n, where L is the length of the string, n is the harmonic number, and λ is the wavelength. Substituting L = 2.0 m and n = 4, we get λ = 0.5 m, which is different from the given wavelength of 1.0 m. Therefore, the statement is false.

Question 3

An open pipe,0.92 m long,vibrates in the second overtone with a frequency of 584 Hz.In this situation,the speed of sound in air,in SI units,is closest to:

Accepted Answer

The answer of An open pipe,0.92 m long,vibrates in the...

Question 4

If a tube filled with air and closed at both ends is 1.60 m long,the longest possible wavelength of the standing waves in this tube is 1.60 m.

Accepted Answer

In a tube closed at both ends, the longest possible wavelength of the standing wave is twice the length of the tube, which would be 3.20 m in this case.

Question 5

A gamma ray (a pulse of electromagnetic energy)has a frequency of 2.42 $\times$ 10²⁰ Hz.What is the ratio of its wavelength to the radius of the nucleus which produced it (radius = 5.0 $\times$10^-13 cm)?

Accepted Answer

The wavelength of a gamma ray is given by the equation:$$\lambda = \frac{c}{f}$$where:* $$\lambda$$ is the wavelength in meters* $$c$$ is the speed of light in meters per second* $$f$$ is the frequency in hertzThe radius of a nucleus is typically on the order of 10^-13 cm.So, the ratio of the wavelength of a gamma ray to the radius of the nucleus which produced it is:$$\frac{\lambda}{r} = \frac{c}{fr} = \frac{3 	imes 10^8 m/s}{(2.42 	imes 10^{20} Hz)(5 	imes 10^{-13} cm)} = 248$$

Question 6

A guitar string is fixed at both ends.If you tighten it to increase its tension,the frequencies of its normal modes will increase but its wavelengths will not be affected.

Accepted Answer

The frequency of a guitar string's normal modes is directly proportional to the tension of the string. As the tension increases, the frequency increases. However, the wavelength of a wave on a string is inversely proportional to the tension of the string. As the tension increases, the wavelength decreases. Therefore, tightening the string to increase its tension will increase the frequencies of its normal modes and decrease its wavelengths.

Question 7

An open pipe,0.95 m long,vibrates in the second overtone with a frequency of 561 Hz.In this situation,the distance from the center of the pipe to the nearest antinode,in cm,is closest to:

Accepted Answer

The second overtone has 3 antinodes and 2 nodes. The distance between adjacent antinodes is 1/4 of the wavelength. The wavelength is twice the length of the pipe, so the distance between adjacent antinodes is 1/2 of the length of the pipe. Therefore, the distance from the center of the pipe to the nearest antinode is 1/4 of the length of the pipe, which is 0.95 m / 4 = 0.2375 m = 23.75 cm. The closest choice is A) 16 cm.

Question 8

A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m.
(a)What is the speed of waves on the string when it is plucked? 
(b)What is the string's fundamental frequency of vibration when plucked?
 (c)What other frequencies will this string allow?

Accepted Answer

The answer of A guitar string 0.65 m long has...

Question 9

If one speaker emits a wave crest at the same time that another one emits a wave trough,these speakers are π/2 out of phase with each other.

Accepted Answer

When one speaker emits a wave crest and the other emits a wave trough, they are π (or 180 degrees) out of phase, not π/2 (or 90 degrees).

Question 10

Situation 16.1
A standing wave of the third overtone is induced in a stopped pipe,1.2 m long.The speed of sound is 340 m/s.
-In Situation 16.1,the frequency of the sound produced by the pipe,in SI units,is closest to:

Accepted Answer

The third overtone in a stopped pipe corresponds to the 7th harmonic. The fundamental frequency is given by $ f_1 = \frac{v}{4L} $. For the 7th harmonic, $ f_7 = 7 \times f_1 = \frac{7 \times 340}{4 \times 1.2} \approx 500 $ Hz.

Question 11

The tension in each of two strings is adjusted so that both vibrate at exactly 666 Hz.The tension in one of the strings is then increased slightly.As a result,six beats per second are heard when both strings vibrate.What is the new frequency of the string that was tightened?

Accepted Answer

The answer of The tension in each of two strings...

Question 12

To demonstrate interference of sound waves,a buzzer is placed in the center of an empty mailing tube that is 0.80 m long.The sound waves emerge from the two ends of the tube in phase and interfere with each other in the region surrounding the tube.When you stand 4.0 m directly in front of the tube,equidistant from its two ends,you hear a loud sound.If you then move parallel to the tube a distance of 1.3 m,the sound nearly disappears.
(a)What's the wavelength of the buzzer's sound waves?
 (b)What's the buzzer's frequency? (Assume the speed of sound in air is 340 m/s. )

Accepted Answer

The answer of To demonstrate interference of sound waves,a buzzer...

Question 13

A 0.335 m string is clamped at both ends.If the lowest standing wave frequency in the string is 326 Hz,what is the wave speed?

Accepted Answer

The lowest standing wave frequency in a string clamped at both ends is given by:$$f_1 = \frac{v}{2L}$$where:* f_1 is the lowest standing wave frequency* v is the wave speed* L is the length of the stringSolving for v, we get:$$v = 2f_1L$$Substituting the given values, we get:$$v = 2(326 	ext{ Hz})(0.335 	ext{ m}) = 218 	ext{ m/s}$$Therefore, the wave speed is 218 m/s.

Question 14

The sound from two loudspeakers is received by a microphone at a point far away along the line through the speakers.The microphone registers maximum intensity when the speakers are 20 cm apart.The sound intensity decreases as the distance between the speakers is increased,reaching zero at a separation of 91 cm.If the distance between the speakers continues to increase,at what separation will the sound intensity again be a maximum?

Accepted Answer

The sound intensity is maximum when the path difference between the waves from the two speakers is a multiple of the wavelength. The first maximum occurs at 20 cm, and the first minimum at 91 cm, indicating a half-wavelength difference of 71 cm. The next maximum will occur at a full wavelength difference of 142 cm (71 cm x 2) from the initial maximum, so 20 cm + 142 cm = 162 cm.

Question 15

If the fourth harmonic for a string fixed at both ends is 220 Hz,the fundamental frequency for this string is 880 Hz.

Accepted Answer

The fundamental frequency can be found by dividing the fourth harmonic frequency by four: 220 Hz / 4 = 55 Hz. Therefore, the statement is false. The fundamental frequency for this string is not 880 Hz.

Question 16

You press two flat pieces of glass together so that a very thin layer of air is trapped between them.Incoming light can reflect from the boundary between the top glass plate and the air,and also from the boundary between the air and the bottom plate;the two reflected waves can then interfere with each other.What is the smallest spacing between the plates that will produce a strong reflection when red light of 680 nm wavelength shines perpendicularly on them?

Accepted Answer

The answer of You press two flat pieces of glass...

Question 17

Two loudspeakers placed 6.0 m apart are driven in phase by an audio oscillator,whose frequency range is 1595 Hz to 2158 Hz.A point P is located 4.7 m from one loudspeaker and 3.6 m from the other.The speed of sound is 344 m/s.The frequency produced by the oscillator,for which destructive interference occurs at point P,in SI units,is closest to:

Accepted Answer

The correct answer is A because the path length difference between the two loudspeakers to point P is 4.7 m - 3.6 m = 1.1 m. For destructive interference, the path length difference must be an odd multiple of half the wavelength, so the wavelength must be 2.2 m. The frequency corresponding to this wavelength is 344 m/s / 2.2 m = 156.8 Hz. The closest frequency in the given range is 1595 Hz, which is an odd multiple of 156.8 Hz.

Question 18

A string fixed at both ends that is vibrating in its eighth harmonic will have 8 antinodes and 9 nodes.

Accepted Answer

In an eighth harmonic, there are eight complete waves and therefore, eight antinodes and nine nodes.

Question 19

Radio station KBOB broadcasts at a frequency of 85.7 MHz on your dial.Since nearly all of the station's audience is due south of the transmitter,the managers of KBOB don't want to waste any energy broadcasting to the east and west.They decide to build two towers,transmitting at exactly the same frequency,aligned on an east-west axis.For engineering reasons,the two towers must be at least 10 meters apart.What's the shortest distance between the towers that will eliminate all broadcast power to the east and west?

Accepted Answer

The answer of Radio station KBOB broadcasts at a frequency...

Question 20

Calculate the light intensity 1.45 m from a 100.0 W light bulb.Assume that the light radiates equally in all directions.

Accepted Answer

The intensity of light is calculated using the formula I = P / (4πr²), where P is the power of the light source and r is the distance from the source. Substituting the given values, I = 100 W / (4π(1.45 m)²) = 3.79 W/m².

Quiz 16: Superposition and Standing Waves

Two speakers next to each other oscillate in phase,one at 404 Hz and the other at 400 Hz.If you stand in front of them,you will hear a sound of frequency 402 Hz that fluctuates between loud and soft with a frequency of 4 Hz.

A string 2.0 m long and fixed at both ends is vibrating in its fourth harmonic in a room at 20C.The wavelength of the sound it produces is 1.0 m.

An open pipe,0.92 m long,vibrates in the second overtone with a frequency of 584 Hz.In this situation,the speed of sound in air,in SI units,is closest to:

If a tube filled with air and closed at both ends is 1.60 m long,the longest possible wavelength of the standing waves in this tube is 1.60 m.

A gamma ray (a pulse of electromagnetic energy) has a frequency of 2.42 $\times$ 10²⁰ Hz.What is the ratio of its wavelength to the radius of the nucleus which produced it (radius = 5.0 $\times$ 10^-13 cm) ?

A guitar string is fixed at both ends.If you tighten it to increase its tension,the frequencies of its normal modes will increase but its wavelengths will not be affected.

An open pipe,0.95 m long,vibrates in the second overtone with a frequency of 561 Hz.In this situation,the distance from the center of the pipe to the nearest antinode,in cm,is closest to:

A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m. (a)What is the speed of waves on the string when it is plucked? (b)What is the string's fundamental frequency of vibration when plucked? (c)What other frequencies will this string allow?

If one speaker emits a wave crest at the same time that another one emits a wave trough,these speakers are π/2 out of phase with each other.

Situation 16.1 A standing wave of the third overtone is induced in a stopped pipe,1.2 m long.The speed of sound is 340 m/s. -In Situation 16.1,the frequency of the sound produced by the pipe,in SI units,is closest to:

The tension in each of two strings is adjusted so that both vibrate at exactly 666 Hz.The tension in one of the strings is then increased slightly.As a result,six beats per second are heard when both strings vibrate.What is the new frequency of the string that was tightened?

A 0.335 m string is clamped at both ends.If the lowest standing wave frequency in the string is 326 Hz,what is the wave speed?

If the fourth harmonic for a string fixed at both ends is 220 Hz,the fundamental frequency for this string is 880 Hz.

A string fixed at both ends that is vibrating in its eighth harmonic will have 8 antinodes and 9 nodes.

Calculate the light intensity 1.45 m from a 100.0 W light bulb.Assume that the light radiates equally in all directions.

Quiz 16: Superposition and Standing Waves

Two speakers next to each other oscillate in phase,one at 404 Hz and the other at 400 Hz.If you stand in front of them,you will hear a sound of frequency 402 Hz that fluctuates between loud and soft with a frequency of 4 Hz.

A string 2.0 m long and fixed at both ends is vibrating in its fourth harmonic in a room at 20C.The wavelength of the sound it produces is 1.0 m.

An open pipe,0.92 m long,vibrates in the second overtone with a frequency of 584 Hz.In this situation,the speed of sound in air,in SI units,is closest to:

If a tube filled with air and closed at both ends is 1.60 m long,the longest possible wavelength of the standing waves in this tube is 1.60 m.

A gamma ray (a pulse of electromagnetic energy) has a frequency of 2.42 ×\times× 1020 Hz.What is the ratio of its wavelength to the radius of the nucleus which produced it (radius = 5.0 ×\times× 10-13 cm) ?

A guitar string is fixed at both ends.If you tighten it to increase its tension,the frequencies of its normal modes will increase but its wavelengths will not be affected.

An open pipe,0.95 m long,vibrates in the second overtone with a frequency of 561 Hz.In this situation,the distance from the center of the pipe to the nearest antinode,in cm,is closest to:

A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m. (a)What is the speed of waves on the string when it is plucked? (b)What is the string's fundamental frequency of vibration when plucked? (c)What other frequencies will this string allow?

If one speaker emits a wave crest at the same time that another one emits a wave trough,these speakers are π/2 out of phase with each other.

Situation 16.1 A standing wave of the third overtone is induced in a stopped pipe,1.2 m long.The speed of sound is 340 m/s. -In Situation 16.1,the frequency of the sound produced by the pipe,in SI units,is closest to:

The tension in each of two strings is adjusted so that both vibrate at exactly 666 Hz.The tension in one of the strings is then increased slightly.As a result,six beats per second are heard when both strings vibrate.What is the new frequency of the string that was tightened?

A 0.335 m string is clamped at both ends.If the lowest standing wave frequency in the string is 326 Hz,what is the wave speed?

If the fourth harmonic for a string fixed at both ends is 220 Hz,the fundamental frequency for this string is 880 Hz.

A string fixed at both ends that is vibrating in its eighth harmonic will have 8 antinodes and 9 nodes.

Calculate the light intensity 1.45 m from a 100.0 W light bulb.Assume that the light radiates equally in all directions.

A gamma ray (a pulse of electromagnetic energy) has a frequency of 2.42 $\times$ 10²⁰ Hz.What is the ratio of its wavelength to the radius of the nucleus which produced it (radius = 5.0 $\times$ 10^-13 cm) ?