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d

20.4 m\text{20.4 m}

Step-by-step solution

3 steps

Here are the answers to your questions:

Part a

To reduce noise from the studio, two physical modifications can be made to the walls

  • Install sound-absorbing materials (such as acoustic panels, foam, or mineral wool) on the walls to reduce reverberation and sound transmission.
  • Increase the thickness or density of the walls, or construct double walls with an air gap in between, which acts as a more effective sound barrier.

Part b

The manager should install a *convex mirror

Reason: A convex mirror provides a wider field of view compared to a plane mirror. This means the manager will be able to see a larger portion of the hallway from the reception desk, thereby improving security and monitoring.

Part c

Arinda's yellow shirt might appear green when green spotlights are turned on because

The color yellow is perceived because it reflects green and red light. When only green spotlights are turned on, the yellow shirt will only reflect the green component of the light, thus appearing green. There is no red light to be reflected, so the "yellow" component derived from red is not seen.

Part d

20.4 m\text{20.4 m}

To calculate the length of the hallway, we will use the distance formula

  1. Identify the given data.

    Speed of sound (vv) = 340 m/s340 \text{ m/s}
    Time (tt) = 0.12 s0.12 \text{ s}

  2. Calculate the total distance traveled by the sound.

    Remember that the sound travels to the end of the hallway and back (echo).

    Total distance=v×t\text{Total distance} = v \times t Total distance=340 m/s×0.12 s\text{Total distance} = 340 \text{ m/s} \times 0.12 \text{ s} Total distance=40.8 m\text{Total distance} = 40.8 \text{ m}
  3. Calculate the length of the hallway.

    The length of the hallway is half of the total distance traveled by the sound.

    Length of hallway=Total distance2\text{Length of hallway} = \frac{\text{Total distance}}{2} Length of hallway=40.8 m2\text{Length of hallway} = \frac{40.8 \text{ m}}{2} Length of hallway=20.4 m\text{Length of hallway} = \boxed{\text{20.4 m}}

    The length of the hallway is 20.4 m.

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