Question

Two friends are standing along a steel fence at a distance of 340 m from each other (Fig. 10.23). Gunjan places her ear over the fence and her friend knocks the fence with a metal object. Using the values of the speed of sound in steel and air given in Table 10.1, calculate the time difference between the sound that reached Gunjan through the air and the steel. Would it have been possible for her to distinguish between the two sounds? (The time interval between two sounds must be at least 0.1 s to be heard separately.)

Answer 1

Distance ($d$): $340\text{ m}$

Speed of sound in air ($v_{\text{air}}$): $340\text{ m/s}$

Speed of sound in steel ($v_{\text{steel}}$): $5000\text{ m/s}$

1. Time taken by sound to reach through air ($t_{\text{air}}$):

$$t_{\text{air}}$$

= $$\frac{d}{v_{\text{air}}}$$

= $$\frac{340\text{ m}}{340\text{ m/s}}$$

= $$1.0\text{ s}$$

2. Time taken by sound to reach through steel ($t_{\text{steel}}$):

$$t_{\text{steel}}$$

= $$\frac{d}{v_{\text{steel}}}$$

 = $$\frac{340\text{ m}}{5000\text{ m/s}}$$

= $$0.068\text{ s}$$

3. Time difference:

$$\Delta t = t_{\text{air}} - t_{\text{steel}}$$

$$ = 1.0\text{ s} - 0.068\text{ s}$$ 

$$ = 0.932\text{ s}$$

4. Conclusion:

Since the time difference ($0.932\text{ s}$) is greater than $0.1\text{ s}$, yes, it would be possible for Gunjan to distinguish between the two sounds.