Exercise 5: A sound is produced at one end of an iron tube of length 1009 m, a person at the other end recieves 2 sounds, one transmitted through iron, and the other transmitted through air, with time difference 2.8 sec . Calculate speed of sound in iron. Given: V=speed of sound in cir=340m/s

To calculate the speed of sound in iron, we can use the given information about the time difference between the two sounds received by the person at the other end of the iron tube.<br /><br />Let's denote the speed of sound in iron as $V_{iron}$ and the speed of sound in air as $V_{air}$. The length of the iron tube is given as 1009 m.<br /><br />The time taken for the sound to travel through iron is given by the formula:<br /><br />$t_{iron} = \frac{L}{V_{iron}}$<br /><br />The time taken for the sound to travel through air is given by the formula:<br /><br />$t_{air} = \frac{L}{V_{air}}$<br /><br />The time difference between the two sounds is given as 2.8 seconds:<br /><br />$t_{air} - t_{iron} = 2.8 \text{ sec}$<br /><br />We can rearrange the above equation to solve for $V_{iron}$:<br /><br />$\frac{L}{V_{air}} - \frac{L}{V_{iron}} = 2.8$<br /><br />Substituting the given value of $V_{air} = 340 \text{ m/s}$, we can solve for $V_{iron}$:<br /><br />$\frac{1009}{340} - \frac{1009}{V_{iron}} = 2.8$<br /><br />Simplifying the equation:<br /><br />$2.98 - \frac{1009}{V_{iron}} = 2.8$<br /><br />$\frac{1009}{V_{iron}} = 0.18$<br /><br />$V_{iron} = \frac{1009}{0.<br /><br />$V_{iron} \approx 5611.11 \text{ m/s}$<br /><br />Therefore, the speed of sound in iron is approximately 5611.11 m/s.