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A student investigates the factors affecting the frequency of sound produced by a vibrating guitar string - Scottish Highers Physics - Question 14 - 2016

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A student investigates the factors affecting the frequency of sound produced by a vibrating guitar string. The guitar string is stretched over two supports and is m... show full transcript

Worked Solution & Example Answer:A student investigates the factors affecting the frequency of sound produced by a vibrating guitar string - Scottish Highers Physics - Question 14 - 2016

Step 1

Calculate the frequency of the sound produced.

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Answer

To find the frequency of the sound produced by the vibrating guitar string, we will use the formula:

f=12LTμf = \frac{1}{2L} \sqrt{\frac{T}{\mu}}

Given:

  • T = 49 N
  • L = 0.550 m
  • \mu = 4.00 \times 10^{-1} : kg , m^{-1}

First, we calculate rac{T}{\mu}:

Tμ=494.00×10−1=122.5 N/kg m−1\frac{T}{\mu} = \frac{49}{4.00 \times 10^{-1}} = 122.5 \: N/kg \, m^{-1}

Now substitute the values into the frequency equation:

f=12×0.550122.5f = \frac{1}{2\times 0.550} \sqrt{122.5}

Calculating:

  • 122.5≈11.07\sqrt{122.5} \approx 11.07
  • Thus,

f=11.1×11.07≈318.2 Hzf = \frac{1}{1.1} \times 11.07 \approx 318.2 \, Hz

Therefore, the frequency of the sound produced is approximately 318.2 Hz.

Step 2

Using the square-ruled paper on Page 36, draw a graph of f against √(T).

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Answer

To draw the graph of frequency ff against  T\, \sqrt{T}, follow these steps:

  1. Set your axes appropriately:

    • Horizontal axis: T\sqrt{T} (N^0.5)
    • Vertical axis: ff (Hz)

  2. Choose suitable scales for both axes to fit all data points.

  3. Plot the points from the table:

    • (3.2, 162)
    • (3.9, 190)
    • (5.0, 230)
    • (5.0, 254)

  4. Ensure that you connect the points with a straight line, if necessary, to show a linear relationship.

  5. Label your axes with appropriate units and title the graph as needed.

Step 3

Use your graph to determine the frequency of the sound produced when the tension in the guitar string is 22 N.

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Answer

To determine the frequency of sound produced at a tension of 22 N:

  1. Calculate  T\, \sqrt{T} for T = 22 N: 22≈4.69 N0.5\sqrt{22} \approx 4.69 \, N^{0.5}

  2. Locate this value on your x-axis in the graph to find the corresponding y-value, which represents the frequency ff.

  3. Read the frequency from the graph at the point where  T=4.69 N0.5\, \sqrt{T} = 4.69 \, N^{0.5}. This will give the approximate frequency for that tension.

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