Question 14 of 23intermediate🔧 ApplyDiagram3 marks

Draw a graph to represent a sound wave for which the density amplitude is 3 units and wavelength is 4 cm.

Correct Answer

To draw the graph of the sound wave:

  1. Draw the X-axis labelled as Distance (cm) and the Y-axis labelled as Density (units).

  2. Draw a horizontal dashed line on the graph representing the average density of the medium.

  3. Since the density amplitude is 3 units, mark the crest (maximum density during compression) at 3 units above the average density line, and the trough (minimum density during rarefaction) at 3 units below the average density line.

  4. Draw a smooth sinusoidal curve starting from the average density line, rising to the crest at +3 units, returning to average, falling to the trough at -3 units, and returning back to average. One complete cycle (from one crest to the next) should span 4 cm on the X-axis, as the wavelength is 4 cm.

Exercise: Revise, Reflect, Refine | Q: 7 | (Page 22)
For More Understanding

Explanation

The textbook explains that a sound wave can be graphically represented by plotting the variation of density of the medium with distance. The amplitude of a sound wave is the maximum change in density compared to the average density. The highest point (crest) represents maximum density (compression) and the lowest point (trough) represents minimum density (rarefaction). The average density is shown as a horizontal dashed line. With amplitude = 3 units, the wave oscillates between +3 and -3 from the average. With wavelength = 4 cm, one complete wave cycle covers 4 cm on the distance axis.

Solution Steps

  1. Step 1: Set up axes - X-axis as Distance (cm), Y-axis as Density (units)

  2. Step 2: Draw a horizontal dashed line for average density

  3. Step 3: Mark crest at +3 units and trough at -3 units from average density line (since amplitude = 3 units)

  4. Step 4: Draw sinusoidal wave where one complete cycle spans 4 cm on X-axis (since wavelength = 4 cm)

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