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![### Oscillations of Air Pressure due to a Musician Playing a Note
**Problem Statement:**
A seated musician plays a C₄ note at 262 Hz. How much time Δt does it take for 571 air pressure maxima to pass a stationary listener?
**Solution:**
To find the required time:
\[ \Delta t = \, \_\_\_\_\_\_\_\_ \, s \]
**Expression of Air Pressure Oscillations:**
To express the air pressure oscillations at a point in space in the given form:
\[ P(t) = P_{\text{max}} \cos(Bt) \]
**Value of B:**
If t is measured in seconds, what value should the quantity B have?
\[ B = \, \_\_\_\_\_\_ \]
**Units for B:**
If \( t \) is measured in seconds, what units should the quantity \( B \) have?
\[ B = \, \_\_\_\_\_\_ \]
Fill in these blanks with correct values and units as per the context of harmonic motion and the given frequency. This problem involves understanding the relationship between frequency, period, and angular frequency in oscillations.
**Explanation:**
- **Frequency (f)** - The number of complete oscillations (cycles) per second.
- **Period (T)** - The time taken for one complete oscillation, given by \( T = \frac{1}{f} \).
- **Angular Frequency (B or ω)** - Describes how quickly the oscillation cycles, given by \( B = 2\pi f \).
Here, \( f = 262 \) Hz and the number of maxima is 571. Use these to calculate the required time and angular frequency.](https://content.bartleby.com/qna-images/question/5039f9f1-9031-4cf0-b840-7355f91f2cd2/5b505bd0-3150-424d-8020-093774442ed8/0dpsa5g.png)
Transcribed Image Text:### Oscillations of Air Pressure due to a Musician Playing a Note
**Problem Statement:**
A seated musician plays a C₄ note at 262 Hz. How much time Δt does it take for 571 air pressure maxima to pass a stationary listener?
**Solution:**
To find the required time:
\[ \Delta t = \, \_\_\_\_\_\_\_\_ \, s \]
**Expression of Air Pressure Oscillations:**
To express the air pressure oscillations at a point in space in the given form:
\[ P(t) = P_{\text{max}} \cos(Bt) \]
**Value of B:**
If t is measured in seconds, what value should the quantity B have?
\[ B = \, \_\_\_\_\_\_ \]
**Units for B:**
If \( t \) is measured in seconds, what units should the quantity \( B \) have?
\[ B = \, \_\_\_\_\_\_ \]
Fill in these blanks with correct values and units as per the context of harmonic motion and the given frequency. This problem involves understanding the relationship between frequency, period, and angular frequency in oscillations.
**Explanation:**
- **Frequency (f)** - The number of complete oscillations (cycles) per second.
- **Period (T)** - The time taken for one complete oscillation, given by \( T = \frac{1}{f} \).
- **Angular Frequency (B or ω)** - Describes how quickly the oscillation cycles, given by \( B = 2\pi f \).
Here, \( f = 262 \) Hz and the number of maxima is 571. Use these to calculate the required time and angular frequency.
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