Question 1

A standing wave of the third overtone is induced in a 1.2-m pipe that is open at one end and closed at the other end.The speed of sound in the pipe is 340 m/s.
(a)How many antinodes are there in the standing wave pattern?
(b)What is the frequency of the sound produced by the pipe in this situation?

Accepted Answer

The answer of A standing wave of the third overtone...

Question 2

By how many decibels does the intensity level of a sound increase when you triple the intensity of a source of sound?

Accepted Answer

The intensity level in decibels (dB) can be calculated using the formula $10 \log_{10}(\frac{I}{I_0})$, where $I$ is the intensity of the sound and $I_0$ is the reference intensity. When you triple the intensity ($I = 3I_0$), the increase in decibels is $10 \log_{10}(3)$, which is approximately 4.8 dB.

Question 3

A crying baby emits sound with an intensity of 8.0 × 10^-8 W/m².Calculate a reasonable estimate for the intensity level from a set of quintuplets (five babies),all crying simultaneously at the same place? The lowest detectable intensity is 1.0 × 10^-12 W/m².

Accepted Answer

The answer of A crying baby emits sound with an...

Question 4

A 2.0-g string that is 0.67 m long is under tension.The string vibrates at 700 Hz tone in its third harmonic,and this vibration causes a sound wave.What is the wavelength of the sound? The speed of sound in air is 344 m/s.

Accepted Answer

The wavelength of the sound can be found using the formula for the speed of sound, $v = f\lambda$, where $v$ is the speed of sound in air (344 m/s), $f$ is the frequency of the sound (700 Hz), and $\lambda$ is the wavelength we need to find. Rearranging the formula to solve for $\lambda$ gives $\lambda = \frac{v}{f}$. Plugging in the given values, $\lambda = \frac{344 \, \text{m/s}}{700 \, \text{Hz}} = 0.49 \, \text{m}$.

Question 5

One of the harmonics of a column of air in a tube that is open at one end and closed at the other has a frequency of 448 Hz,and the next higher harmonic has a frequency of 576 Hz.What is the fundamental frequency of the air column in this tube?

Accepted Answer

The fundamental frequency (first harmonic) for a tube open at one end and closed at the other is given by the difference between any two consecutive harmonics, because the harmonics in such a tube are odd multiples of the fundamental frequency. The difference between 576 Hz and 448 Hz is 128 Hz, which represents the frequency difference between two consecutive harmonics (3rd and 4th, for example). Since the tube supports odd harmonics only (1st, 3rd, 5th, etc.), the next lower harmonic from the 3rd (which would be the 1st or fundamental) would be two steps back, or 128 Hz / 2 = 64 Hz.

Question 6

A sound of 40 decibels is

Accepted Answer

The decibel scale is logarithmic, meaning a 10-decibel increase represents a sound that is 10 times more intense. Therefore, a 20-decibel increase (from 20 to 40 decibels) indicates the sound is 10 times 10, or 100 times more intense.

Question 7

An organ pipe open at both ends has a length of 0.80 m.If the velocity of sound in air is $340 \mathrm {~m} / \mathrm { s } \text {, }$ what is the frequency of the second harmonic of this pipe?

Accepted Answer

The second harmonic of an organ pipe open at both ends corresponds to the first overtone, which has a wavelength equal to the length of the pipe. The formula for frequency is $f = \frac{v}{\lambda}$, where $v$ is the velocity of sound and $\lambda$ is the wavelength. For the second harmonic, $\lambda = \frac{2L}{2}$ (where $L$ is the length of the pipe), so $\lambda = L = 0.80 m$. Therefore, $f = \frac{340 m/s}{0.80 m} = 425 Hz$.

Question 8

Consider two pipes of the same length: one pipe is open at both ends and the other pipe is closed on one end but open at the other end.If the fundamental frequency of the totally open pipe is 300 Hz,what is the fundamental frequency of the other pipe?

Accepted Answer

The fundamental frequency of a pipe open at both ends is given by $f = \frac{v}{2L}$, where $v$ is the speed of sound and $L$ is the length of the pipe. For a pipe closed at one end, the fundamental frequency is given by $f = \frac{v}{4L}$, which is half the frequency of the open pipe because the closed pipe supports only odd harmonics. Therefore, if the open pipe has a fundamental frequency of 300 Hz, the closed pipe's fundamental frequency will be half of that, which is 150 Hz.

Question 9

Two people are talking at a distance of 3.0 m from where you are,and you measure the sound intensity as 1.1 × 10^-7 W/m².Another student is 4.0 m away from the talkers.Calculate a reasonable estimate for the sound intensity that the other student measures.

Accepted Answer

The sound intensity $I$ is inversely proportional to the square of the distance $r$ from the source, as given by the formula $I \propto \frac{1}{r^2}$. Therefore, if the distance increases, the intensity decreases. Given the initial intensity is $1.1 \times 10^{-7} \, \text{W/m}^2$ at 3.0 m, the intensity at 4.0 m can be calculated using the ratio $\frac{I_1}{I_2} = \frac{r_2^2}{r_1^2}$, leading to the correct choice being the one that represents a decrease in intensity consistent with the increase in distance.

Question 10

One of the harmonics of a column of air in a tube that is open at one end and closed at the other has a frequency of 448 Hz,and the next higher harmonic has a frequency of 576 Hz.How long is the tube? The speed of sound in air is 343 m/s.

Accepted Answer

In a column of air in a tube that is open at one end and closed at the other, the length of the tube (L) is related to the wavelength (λ) of the sound wave produced by the tube by the equation:

L = (n/2) * λ

where n is the harmonic number (an integer representing the number of half-wavelengths of the sound wave that fit into the length of the tube).

From the problem, we know that the first harmonic (n = 1) has a frequency of 448 Hz and the second harmonic (n = 2) has a frequency of 576 Hz.

The speed of sound in air is given as 343 m/s.

Using the formula for the speed of sound,

v = fλ

where v is the speed of sound, f is the frequency, and λ is the wavelength, we can find the wavelength of each harmonic:

For the first harmonic:

λ = v/f = 343/448 = 0.766 m

For the second harmonic:

λ = v/f = 343/576 = 0.596 m

Substituting these values into the equation for the length of the tube, we have:

For the first harmonic:

L = (n/2) * λ = (1/2) * 0.766 = 0.383 m

For the second harmonic:

L = (n/2) * λ = (2/2) * 0.596 = 0.596 m

Since the tube is open at one end and closed at the other, the first harmonic is the fundamental frequency (i.e. the frequency with the longest wavelength that can produce a standing wave in the tube). Thus, the length of the tube must be equal to one-fourth of the wavelength of the first harmonic:

L = λ/4 = 0.766/4 = 0.1915 m

Multiplying this by 7 (to get the length of the tube that produces the seventh harmonic, which has a frequency of 448 Hz), we get:

L = 0.1915 * 7 = 1.34 m

Therefore, the best choice is A) 1.34 m.

Question 11

A pipe that is 0.92 m long and open at both ends vibrates in the second overtone with a frequency of $584 \mathrm {~Hz}$ What is the speed of sound in the air in this pipe?

Accepted Answer

The second overtone has $n=3$. The frequency of the second overtone is given by:$$f_3=\frac{3v}{2L}$$where $v$ is the speed of sound and $L$ is the length of the pipe. Substituting the given values, we get:$$584 \mathrm {~Hz}=\frac{3v}{2(0.92 \mathrm {~m})}$$Solving for $v$, we get:$$v=353 \mathrm {~m/s}$$

Question 12

An organ pipe that is 1.75 m long and open at both ends produces sound of frequency 303 Hz when resonating in its second overtone.What is the speed of sound in the room?

Accepted Answer

The answer of An organ pipe that is 1.75 m...

Question 13

One of the harmonics of a column of air in a tube that is open at both ends has a frequency of 448 Hz,and the next higher harmonic has a frequency of 576 Hz.What is the fundamental frequency of the air column in this tube?

Accepted Answer

The answer of One of the harmonics of a column...

Question 14

A certain glass window reduces the intensity level of the sound from 72 dB to 47 dB.By what factor is the acoustic power reduced by this glass window?

Accepted Answer

The answer of A certain glass window reduces the intensity...

Question 15

What is the length of the shortest pipe closed on one end and open at the other end that will have a fundamental frequency of 0.060 kHz on a day when the speed of sound is 340 m/s?

Accepted Answer

The formula to calculate the fundamental frequency of a closed-open pipe is:

f1 = v/4L

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

Rearranging the formula, we get:

L = v/4f1

Substituting the given values, we get:

L = (340 m/s)/(4 × 0.060 kHz) = 1.42 m

Therefore, the length of the shortest pipe closed on one end and open at the other end that will have a fundamental frequency of 0.060 kHz on a day when the speed of sound is 340 m/s is 1.42 m.

Question 16

A certain factory whistle can be heard up to a distance of 9.8 km.Assuming that the acoustic output of the whistle is uniform in all directions,at what distance from the factory is the intensity level of the whistle sound equal to 25 dB? The threshold of human hearing is 1.0 × 10^-12 W/m².

Accepted Answer

The answer of A certain factory whistle can be heard...

Question 17

An organ pipe closed at one end and open at the other end has two successive harmonics with frequencies of 2170 Hz and 2790 Hz.What is the fundamental frequency of the pipe?

Accepted Answer

The answer of An organ pipe closed at one end...

Question 18

A string that is 0.15 m long and fixed at both ends is vibrating in its n = 5 harmonic.The sound from this string excites a pipe that is $0.82 \mathrm {~m}$ long and open at both ends into its second overtone resonance.What is the distance between a node and an adjacent antinode,in the string? The speed of sound in air is 345 m/s.

Accepted Answer

For the string vibrating in its n = 5 harmonic, the wavelength $\lambda$ can be found using the relationship that the length of the string $L$ is equal to $n\lambda/2$, where $n$ is the harmonic number. Given $L = 0.15$ m and $n = 5$, we have $0.15 = 5\lambda/2$, solving for $\lambda$ gives $\lambda = 0.06$ m. The distance between a node and an adjacent antinode is $\lambda/4$, which is $0.06/4 = 0.015$ m or 15 mm.

Question 19

If the intensity level of one trombone is 70 dB,calculate a reasonable estimate for the intensity level of 76 trombones all playing simultaneously in the same place?

Accepted Answer

Doubling the number of sound sources (like trombones) increases the intensity level by about 3 dB. Since 76 is 2^6 (or 64) times one trombone, you add 3 dB six times to the original 70 dB, resulting in an increase of 18 dB (6*3 dB). Therefore, the total intensity level is 70 dB + 18 dB = 88 dB, which is closest to 89 dB (option B).

Question 20

A long-term exposure to the sound of a riveting machine can cause your threshold of hearing to shift from 0 dB to 30 dB.What is the sound intensity of a 30-dB sound? The normal lowest detectable intensity is 1.0 × 10^-12 W/m².

Accepted Answer

The answer of A long-term exposure to the sound of...

Quiz 21: Mechanical Waves

A standing wave of the third overtone is induced in a 1.2-m pipe that is open at one end and closed at the other end.The speed of sound in the pipe is 340 m/s. (a)How many antinodes are there in the standing wave pattern? (b)What is the frequency of the sound produced by the pipe in this situation?

By how many decibels does the intensity level of a sound increase when you triple the intensity of a source of sound?

A crying baby emits sound with an intensity of 8.0 × 10^-8 W/m².Calculate a reasonable estimate for the intensity level from a set of quintuplets (five babies) ,all crying simultaneously at the same place? The lowest detectable intensity is 1.0 × 10^-12 W/m².

A 2.0-g string that is 0.67 m long is under tension.The string vibrates at 700 Hz tone in its third harmonic,and this vibration causes a sound wave.What is the wavelength of the sound? The speed of sound in air is 344 m/s.

One of the harmonics of a column of air in a tube that is open at one end and closed at the other has a frequency of 448 Hz,and the next higher harmonic has a frequency of 576 Hz.What is the fundamental frequency of the air column in this tube?

A sound of 40 decibels is

An organ pipe open at both ends has a length of 0.80 m.If the velocity of sound in air is $340 \mathrm {~m} / \mathrm { s } \text {, }$ what is the frequency of the second harmonic of this pipe?

Consider two pipes of the same length: one pipe is open at both ends and the other pipe is closed on one end but open at the other end.If the fundamental frequency of the totally open pipe is 300 Hz,what is the fundamental frequency of the other pipe?

Two people are talking at a distance of 3.0 m from where you are,and you measure the sound intensity as 1.1 × 10^-7 W/m².Another student is 4.0 m away from the talkers.Calculate a reasonable estimate for the sound intensity that the other student measures.

One of the harmonics of a column of air in a tube that is open at one end and closed at the other has a frequency of 448 Hz,and the next higher harmonic has a frequency of 576 Hz.How long is the tube? The speed of sound in air is 343 m/s.

A pipe that is 0.92 m long and open at both ends vibrates in the second overtone with a frequency of $584 \mathrm {~Hz}$ What is the speed of sound in the air in this pipe?

An organ pipe that is 1.75 m long and open at both ends produces sound of frequency 303 Hz when resonating in its second overtone.What is the speed of sound in the room?

One of the harmonics of a column of air in a tube that is open at both ends has a frequency of 448 Hz,and the next higher harmonic has a frequency of 576 Hz.What is the fundamental frequency of the air column in this tube?

A certain glass window reduces the intensity level of the sound from 72 dB to 47 dB.By what factor is the acoustic power reduced by this glass window?

What is the length of the shortest pipe closed on one end and open at the other end that will have a fundamental frequency of 0.060 kHz on a day when the speed of sound is 340 m/s?

A certain factory whistle can be heard up to a distance of 9.8 km.Assuming that the acoustic output of the whistle is uniform in all directions,at what distance from the factory is the intensity level of the whistle sound equal to 25 dB? The threshold of human hearing is 1.0 × 10^-12 W/m².

An organ pipe closed at one end and open at the other end has two successive harmonics with frequencies of 2170 Hz and 2790 Hz.What is the fundamental frequency of the pipe?

If the intensity level of one trombone is 70 dB,calculate a reasonable estimate for the intensity level of 76 trombones all playing simultaneously in the same place?

A long-term exposure to the sound of a riveting machine can cause your threshold of hearing to shift from 0 dB to 30 dB.What is the sound intensity of a 30-dB sound? The normal lowest detectable intensity is 1.0 × 10^-12 W/m².

Quiz 21: Mechanical Waves

A standing wave of the third overtone is induced in a 1.2-m pipe that is open at one end and closed at the other end.The speed of sound in the pipe is 340 m/s. (a)How many antinodes are there in the standing wave pattern? (b)What is the frequency of the sound produced by the pipe in this situation?

By how many decibels does the intensity level of a sound increase when you triple the intensity of a source of sound?

A crying baby emits sound with an intensity of 8.0 × 10-8 W/m2.Calculate a reasonable estimate for the intensity level from a set of quintuplets (five babies) ,all crying simultaneously at the same place? The lowest detectable intensity is 1.0 × 10-12 W/m2.

A 2.0-g string that is 0.67 m long is under tension.The string vibrates at 700 Hz tone in its third harmonic,and this vibration causes a sound wave.What is the wavelength of the sound? The speed of sound in air is 344 m/s.

One of the harmonics of a column of air in a tube that is open at one end and closed at the other has a frequency of 448 Hz,and the next higher harmonic has a frequency of 576 Hz.What is the fundamental frequency of the air column in this tube?

A sound of 40 decibels is

An organ pipe open at both ends has a length of 0.80 m.If the velocity of sound in air is 340 m/s, 340 \mathrm {~m} / \mathrm { s } \text {, }340 m/s, what is the frequency of the second harmonic of this pipe?

Consider two pipes of the same length: one pipe is open at both ends and the other pipe is closed on one end but open at the other end.If the fundamental frequency of the totally open pipe is 300 Hz,what is the fundamental frequency of the other pipe?

Two people are talking at a distance of 3.0 m from where you are,and you measure the sound intensity as 1.1 × 10-7 W/m2.Another student is 4.0 m away from the talkers.Calculate a reasonable estimate for the sound intensity that the other student measures.

One of the harmonics of a column of air in a tube that is open at one end and closed at the other has a frequency of 448 Hz,and the next higher harmonic has a frequency of 576 Hz.How long is the tube? The speed of sound in air is 343 m/s.

A pipe that is 0.92 m long and open at both ends vibrates in the second overtone with a frequency of 584 Hz584 \mathrm {~Hz}584 Hz What is the speed of sound in the air in this pipe?

An organ pipe that is 1.75 m long and open at both ends produces sound of frequency 303 Hz when resonating in its second overtone.What is the speed of sound in the room?

One of the harmonics of a column of air in a tube that is open at both ends has a frequency of 448 Hz,and the next higher harmonic has a frequency of 576 Hz.What is the fundamental frequency of the air column in this tube?

A certain glass window reduces the intensity level of the sound from 72 dB to 47 dB.By what factor is the acoustic power reduced by this glass window?

What is the length of the shortest pipe closed on one end and open at the other end that will have a fundamental frequency of 0.060 kHz on a day when the speed of sound is 340 m/s?

A certain factory whistle can be heard up to a distance of 9.8 km.Assuming that the acoustic output of the whistle is uniform in all directions,at what distance from the factory is the intensity level of the whistle sound equal to 25 dB? The threshold of human hearing is 1.0 × 10-12 W/m2.

An organ pipe closed at one end and open at the other end has two successive harmonics with frequencies of 2170 Hz and 2790 Hz.What is the fundamental frequency of the pipe?

If the intensity level of one trombone is 70 dB,calculate a reasonable estimate for the intensity level of 76 trombones all playing simultaneously in the same place?

A long-term exposure to the sound of a riveting machine can cause your threshold of hearing to shift from 0 dB to 30 dB.What is the sound intensity of a 30-dB sound? The normal lowest detectable intensity is 1.0 × 10-12 W/m2.

A crying baby emits sound with an intensity of 8.0 × 10^-8 W/m².Calculate a reasonable estimate for the intensity level from a set of quintuplets (five babies) ,all crying simultaneously at the same place? The lowest detectable intensity is 1.0 × 10^-12 W/m².

An organ pipe open at both ends has a length of 0.80 m.If the velocity of sound in air is $340 \mathrm {~m} / \mathrm { s } \text {, }$ what is the frequency of the second harmonic of this pipe?

Two people are talking at a distance of 3.0 m from where you are,and you measure the sound intensity as 1.1 × 10^-7 W/m².Another student is 4.0 m away from the talkers.Calculate a reasonable estimate for the sound intensity that the other student measures.

A pipe that is 0.92 m long and open at both ends vibrates in the second overtone with a frequency of $584 \mathrm {~Hz}$ What is the speed of sound in the air in this pipe?

A certain factory whistle can be heard up to a distance of 9.8 km.Assuming that the acoustic output of the whistle is uniform in all directions,at what distance from the factory is the intensity level of the whistle sound equal to 25 dB? The threshold of human hearing is 1.0 × 10^-12 W/m².

A long-term exposure to the sound of a riveting machine can cause your threshold of hearing to shift from 0 dB to 30 dB.What is the sound intensity of a 30-dB sound? The normal lowest detectable intensity is 1.0 × 10^-12 W/m².