College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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**Problem:**

A seated musician plays a G₅ note at 784 Hz. How much time Δt does it take for 496 air pressure maxima to pass a stationary listener?

\[ \Delta t = \_\_\_\_ \, \text{s} \]

**Question:**

You would like to express the air pressure oscillations at a point in space in the given form.

\[ P(t) = P_{\text{max}} \cos (Bt) \]

If \( t \) is measured in seconds, what value should the quantity \( B \) have?

\[ B = \_\_\_\_ \]

If \( t \) is measured in seconds, what units should the quantity \( B \) have?

---

**Explanation:**

The problem involves understanding the relationship between frequency, time, and air pressure oscillations in relation to sound waves. The first part requires calculating the time it takes for a certain number of wave peaks (maxima) to pass by, given the frequency of the sound wave.

In the second part, the task is to determine the angular frequency \( B \) for a cosine function describing pressure oscillations, which involves converting the frequency from Hz to radians per second. Understanding units and their implications is crucial for interpreting these quantities physically.
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Transcribed Image Text:**Problem:** A seated musician plays a G₅ note at 784 Hz. How much time Δt does it take for 496 air pressure maxima to pass a stationary listener? \[ \Delta t = \_\_\_\_ \, \text{s} \] **Question:** You would like to express the air pressure oscillations at a point in space in the given form. \[ P(t) = P_{\text{max}} \cos (Bt) \] If \( t \) is measured in seconds, what value should the quantity \( B \) have? \[ B = \_\_\_\_ \] If \( t \) is measured in seconds, what units should the quantity \( B \) have? --- **Explanation:** The problem involves understanding the relationship between frequency, time, and air pressure oscillations in relation to sound waves. The first part requires calculating the time it takes for a certain number of wave peaks (maxima) to pass by, given the frequency of the sound wave. In the second part, the task is to determine the angular frequency \( B \) for a cosine function describing pressure oscillations, which involves converting the frequency from Hz to radians per second. Understanding units and their implications is crucial for interpreting these quantities physically.
**Question:**

If \( t \) is measured in seconds, what units should the quantity \( B \) have?

**Options:**

- seconds
- radians
- meters
- meters per second
- radians per second

---

This question examines the appropriate units for a given quantity \( B \) when time \( t \) is measured in seconds. Understanding the physical context of \( B \) is crucial for determining the correct units from the provided options.
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Transcribed Image Text:**Question:** If \( t \) is measured in seconds, what units should the quantity \( B \) have? **Options:** - seconds - radians - meters - meters per second - radians per second --- This question examines the appropriate units for a given quantity \( B \) when time \( t \) is measured in seconds. Understanding the physical context of \( B \) is crucial for determining the correct units from the provided options.
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