1. Two single-frequency sounds are emitted from separate speakers, both of which are equipped with wheels that allow them to be moved along a common pair of straight-line tracks, and their positions recorded, as shown in the diagram. The speakers are driven by the same source, producing monotones from the speakers that are in phase and at the same frequency. The speaker at x₁ = 0 cm remains at rest, while the other speaker is rolled forward until a listener positioned in front of the speakers hears silence. The speaker is then rolled forward another 215 cm and is stopped at a new position. In this configuration the listener once again hears silence. The speed of sound in this region is 344 m/s. x = x₁ x = x₂ (a) Find the frequency of the tone emitted by the speakers. (b) In the process of rolling the front speaker to its new position, the rear speaker is turned off and the rolling speaker is left on. If its rolling speed is held constant and it takes 0.250 s to get from its old position to the new one, find the frequency of the moving front speaker as heard by the listener.

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### Problem Statement for Educational Website

1. **Experiment Setup:**
   - Two single-frequency sounds are emitted from separate speakers, each equipped with wheels for movement along straight tracks.
   - The speakers are synchronized to produce monotones at the same frequency that are in phase.
   - Initially, one speaker remains stationary at \( x_1 = 0 \, \text{cm} \), while the other speaker is moved forward until silence is heard by a listener positioned in front of the speakers.
   - The moving speaker advances an additional 215 cm, stopping at a new position where silence is again observed.
   - The speed of sound in this setting is 344 m/s.

   - **Diagram Description:**
     - The diagram shows two speaker cars. The left car is at position \( x = x_1 \) and emits sound waves in red, while the right car is at position \( x = x_2 \) and emits sound waves in blue.

2. **Questions:**
   - (a) Calculate the frequency of the tone emitted by the speakers.
   - (b) During the speaker's movement to the new position, the rear speaker is deactivated, leaving only the moving speaker active. If the moving speaker travels at a constant speed and takes 0.250 s to reach the new position, determine the frequency of the moving speaker as perceived by the listener.
Transcribed Image Text:### Problem Statement for Educational Website 1. **Experiment Setup:** - Two single-frequency sounds are emitted from separate speakers, each equipped with wheels for movement along straight tracks. - The speakers are synchronized to produce monotones at the same frequency that are in phase. - Initially, one speaker remains stationary at \( x_1 = 0 \, \text{cm} \), while the other speaker is moved forward until silence is heard by a listener positioned in front of the speakers. - The moving speaker advances an additional 215 cm, stopping at a new position where silence is again observed. - The speed of sound in this setting is 344 m/s. - **Diagram Description:** - The diagram shows two speaker cars. The left car is at position \( x = x_1 \) and emits sound waves in red, while the right car is at position \( x = x_2 \) and emits sound waves in blue. 2. **Questions:** - (a) Calculate the frequency of the tone emitted by the speakers. - (b) During the speaker's movement to the new position, the rear speaker is deactivated, leaving only the moving speaker active. If the moving speaker travels at a constant speed and takes 0.250 s to reach the new position, determine the frequency of the moving speaker as perceived by the listener.
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