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A stationary wave is formed on a stretched wire - AQA - A-Level Physics - Question 3 - 2019 - Paper 3

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A stationary wave is formed on a stretched wire. Figure 14 shows the wire, fixed at one end, supported by two bridges and passing over a pulley. A 0.500 kg mass is... show full transcript

Worked Solution & Example Answer:A stationary wave is formed on a stretched wire - AQA - A-Level Physics - Question 3 - 2019 - Paper 3

Step 1

Determine $f$, the frequency of the alternating pd.

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Answer

To find the frequency ff, we can use the time-base settings from Figure 16. The time setting is 10 ms cm−1^{-1}, and one full waveform (one complete cycle) spans a distance of 5 cm (5 divisions on the oscilloscope). The time period TT for this waveform can be calculated as:

T=5extcmimes10extmscm−1=50extms=0.050extsT = 5 ext{ cm} imes 10 ext{ ms cm}^{-1} = 50 ext{ ms} = 0.050 ext{ s}

The frequency ff can then be found using the formula:

f = rac{1}{T} = rac{1}{0.050 ext{ s}} = 20 ext{ Hz}

Step 2

Determine the wavelength $ abla$ of the stationary wave shown in Figure 17.

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Answer

From Figure 17, we note that the stationary wave exhibits three complete wavelengths between the two bridges, which measures approximately 24 cm. Thus, the wavelength abla abla can be calculated as:

abla = rac{24 ext{ cm}}{3} = 8 ext{ cm} = 0.08 ext{ m}$$

Step 3

Determine $c$.

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Answer

The wave speed cc is related to the frequency ff and wavelength abla abla by the equation:

abla$$ Substituting in our values: $$c = 20 ext{ Hz} imes 0.08 ext{ m} = 1.6 ext{ m s}^{-1}$$

Step 4

Determine, in kg m$^{-1}$, the mass per unit length of the wire.

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Answer

Given the mass per unit length (ho ho) is provided as 3.54 × 103^{3} kg m−1^{-1}, we can state:

extmassperunitlength=3.54imes103extkgm−1 ext{mass per unit length} = 3.54 imes 10^{3} ext{ kg m}^{-1}

Step 5

Calculate the diameter $d$ of the rod.

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Answer

To obtain the diameter dd, average the readings from the calipers indicated in Figure 18. For example, if the readings indicate 8.71 mm and 8.16 mm:

d = rac{8.71 ext{ mm} + 8.16 ext{ mm}}{2} = 8.445 ext{ mm}

Step 6

Describe relevant procedures to limit the effect of random error in the result for $d$.

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Answer

To limit random error in measuring diameter dd, the following procedures can be implemented:

  • Take multiple measurements at different positions along the rod and calculate an average.
  • Ensure the calipers are properly calibrated before use to eliminate systematic errors.
  • Measure the diameter in different orientations to ensure uniformity.

Step 7

Determine the density of the rod.

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Answer

To find the density, use the formula:

ho = rac{ ext{mass}}{ ext{volume}}$$ Given that mass per unit length is 3.54 × 10$^{3}$ kg m$^{-1}$, and assuming a cross-sectional area $A$ (calculated from part earlier), we can express the density as: $$ ext{density} = rac{3.54 imes 10^{3}}{A}$$

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