A steady sound with a frequency of f = 750 Hz is produced by a source located far from an open doorway set in a sound- absorbing wall. The sound waves pass through the w = 1.18 m-wide doorway. (Assume the speed of sound is 343 m/s.) (a) If a person walks parallel to the wall beyond the open doorway, how many diffraction minima will she encounter? (b) What are the angular directions (in degrees) of these diffraction minima? (Enter the magnitudes from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks. Do not enter any duplicate numerical values.) smallest 土 largest
A steady sound with a frequency of f = 750 Hz is produced by a source located far from an open doorway set in a sound- absorbing wall. The sound waves pass through the w = 1.18 m-wide doorway. (Assume the speed of sound is 343 m/s.) (a) If a person walks parallel to the wall beyond the open doorway, how many diffraction minima will she encounter? (b) What are the angular directions (in degrees) of these diffraction minima? (Enter the magnitudes from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks. Do not enter any duplicate numerical values.) smallest 土 largest
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![### Sound Diffraction Through an Open Doorway
#### Problem Statement
A steady sound with a frequency of \( f = 750 \) Hz is produced by a source located far from an open doorway set in a sound-absorbing wall. The sound waves pass through the \( w = 1.18 \) m-wide doorway. (Assume the speed of sound is 343 m/s.)
**(a)** If a person walks parallel to the wall beyond the open doorway, how many diffraction minima will she encounter?
[Answer Text Box]
**(b)** What are the angular directions (in degrees) of these diffraction minima? (Enter the magnitudes from smallest to largest, starting with the first answer blank. Enter NONE in any remaining answer blanks. Do not enter any duplicate numerical values.)
| smallest \( \pm \) | [Answer Text Box]° |
|-------------------------|-------------------------------|
| \( \pm \) | [Answer Text Box]° |
|-------------------------|-------------------------------|
| \( \pm \) | [Answer Text Box]° |
|-------------------------|-------------------------------|
| largest \( \pm \) | [Answer Text Box]° |
|-------------------------|-------------------------------|
#### Explanation:
When sound waves encounter an obstacle, such as the edges of an open doorway, they bend around the edges and create a diffraction pattern. The minima in this pattern can be determined by the angle \( \theta \) where destructive interference occurs.
For a doorway of width \( w \):
\[ \sin(\theta) = \frac{m \lambda}{w} \]
where \( \lambda \) is the wavelength of the sound and \( m \) is the order of the minimum ( \( m = \pm 1, \pm 2, \pm 3, \ldots \)).
Given:
- Frequency, \( f = 750 \) Hz
- Speed of sound, \( v = 343 \) m/s
- Door width, \( w = 1.18 \) m
Calculate the wavelength:
\[ \lambda = \frac{v}{f} \]
\[ \lambda = \frac{343 \, \text{m/s}}{750 \, \text{Hz}} \]
\[ \lambda \approx 0.457 \, \text{m} \]
By substituting the values into the interference condition, diffraction minima angles can be calculated.
This forms the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feafc6826-5c88-4b32-b630-d072d1855c17%2Fd9c6a1f6-9872-48df-8a43-b10171eb6845%2Foof2q5v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Sound Diffraction Through an Open Doorway
#### Problem Statement
A steady sound with a frequency of \( f = 750 \) Hz is produced by a source located far from an open doorway set in a sound-absorbing wall. The sound waves pass through the \( w = 1.18 \) m-wide doorway. (Assume the speed of sound is 343 m/s.)
**(a)** If a person walks parallel to the wall beyond the open doorway, how many diffraction minima will she encounter?
[Answer Text Box]
**(b)** What are the angular directions (in degrees) of these diffraction minima? (Enter the magnitudes from smallest to largest, starting with the first answer blank. Enter NONE in any remaining answer blanks. Do not enter any duplicate numerical values.)
| smallest \( \pm \) | [Answer Text Box]° |
|-------------------------|-------------------------------|
| \( \pm \) | [Answer Text Box]° |
|-------------------------|-------------------------------|
| \( \pm \) | [Answer Text Box]° |
|-------------------------|-------------------------------|
| largest \( \pm \) | [Answer Text Box]° |
|-------------------------|-------------------------------|
#### Explanation:
When sound waves encounter an obstacle, such as the edges of an open doorway, they bend around the edges and create a diffraction pattern. The minima in this pattern can be determined by the angle \( \theta \) where destructive interference occurs.
For a doorway of width \( w \):
\[ \sin(\theta) = \frac{m \lambda}{w} \]
where \( \lambda \) is the wavelength of the sound and \( m \) is the order of the minimum ( \( m = \pm 1, \pm 2, \pm 3, \ldots \)).
Given:
- Frequency, \( f = 750 \) Hz
- Speed of sound, \( v = 343 \) m/s
- Door width, \( w = 1.18 \) m
Calculate the wavelength:
\[ \lambda = \frac{v}{f} \]
\[ \lambda = \frac{343 \, \text{m/s}}{750 \, \text{Hz}} \]
\[ \lambda \approx 0.457 \, \text{m} \]
By substituting the values into the interference condition, diffraction minima angles can be calculated.
This forms the
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