A seated musician plays a G, note at 784 Hz. How much time At does it take for 496 air pressure maxima to pass a stationary listener? At = You would like to express the air pressure oscillations at a point in space in the given form. P (t) = Pmax Cos (Bt) If t is measured in seconds, what value should the quantity B have?

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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.
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.
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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