Question

Observe the illustration of a wave.

• [(a)] Which type of mechanical wave is this?
• [(b)] What do the letters C and R indicate?
• [(c)] If the distance between two consecutive ‘C’ of the wave is \(0.01\ \text{m}\), which is travelling with a speed of \(350\ \text{m/s}\), will it be audible to humans? Justify your answer by mathematical calculation.

Hint:

Frequency \(> 20{,}000\ \text{Hz}\) → Ultrasonic (not audible)

Answer 1

(a) Type of wave
Concept:
The diagram shows regions of compression (C) and rarefaction (R), which are characteristics of longitudinal waves. Answer: \[ \text{Longitudinal wave} \] (b) Meaning of C and R

• C → Compression (region of high pressure/density)
• R → Rarefaction (region of low pressure/density)

(c) Audibility of the wave
Step 1: Given data}
\[ \lambda = 0.01\ \text{m}, \quad v = 350\ \text{m/s} \] Step 2: Formula}
\[ v = f \lambda \Rightarrow f = \frac{v}{\lambda} \] Step 3: Calculation}
\[ f = \frac{350}{0.01} = 35000\ \text{Hz} \] Step 4: Compare with human hearing range}
Human audible range: \[ 20\ \text{Hz} \text{ to } 20000\ \text{Hz} \] Step 5: Conclusion}
\[ 35000\ \text{Hz}>20000\ \text{Hz} \] So, the sound is: \[ \text{Not audible (ultrasonic)} \]